Optics
Encyclopedia
Optics is the branch of physics
which involves the behavior and properties of light
, including its interactions with matter
and the construction of instruments that use or detect
it. Optics usually describes the behavior of visible, ultraviolet
, and infrared
light. Because light is an electromagnetic wave, other forms of electromagnetic radiation
such as X-ray
s, microwave
s, and radio wave
s exhibit similar properties.
Most optical phenomena can be accounted for using the classical electromagnetic
description of light. Complete electromagnetic descriptions of light are, however, often difficult to apply in practice. Practical optics is usually done using simplified models. The most common of these, geometric optics, treats light as a collection of ray
s that travel in straight lines and bend when they pass through or reflect from surfaces. Physical optics
is a more comprehensive model of light, which includes wave
effects such as diffraction
and interference that cannot be accounted for in geometric optics. Historically, the ray-based model of light was developed first, followed by the wave model of light. Progress in electromagnetic theory in the 19th century led to the discovery that light waves were in fact electromagnetic radiation.
Some phenomena depend on the fact that light has both wave-like and particle-like properties. Explanation of these effects requires quantum mechanics
. When considering light's particle-like properties, the light is modeled as a collection of particles called "photon
s". Quantum optics
deals with the application of quantum mechanics to optical systems.
Optical science is relevant to and studied in many related disciplines including astronomy
, various engineering
fields, photography
, and medicine
(particularly ophthalmology
and optometry
). Practical applications of optics are found in a variety of technologies and everyday objects, including mirror
s, lenses, telescopes
, microscope
s, lasers, and fiber optics.
ians and Mesopotamia
ns. The earliest known lenses were made from polished crystal, often quartz
, and have been dated as early as 700 BC for Assyria
n lenses such as the Layard/Nimrud lens
. The ancient Romans and Greeks
filled glass spheres with water to make lenses. These practical developments were followed by the development of theories of light and vision by ancient Greek
and Indian
philosophers, and the development of geometrical optics
in the Greco-Roman world
. The word optics comes from the ancient Greek
word , meaning appearance or look. Plato
first articulated emission theory
, the idea that visual perception
is accomplished by rays emitted by the eyes. He also commented on the parity
reversal of mirrors in Timaeus
. Some hundred years later, Euclid
wrote a treatise entitled Optics wherein he described the mathematical rules of perspective
and describes the effects of refraction qualitatively. Ptolemy
, in his treatise Optics, summarizes much of Euclid and goes on to describe a way to measure the angle of refraction, though he failed to notice the empirical relationship between it and the angle of incidence.
During the Middle Ages
, Greek ideas about optics were resurrected and extended by writers in the Muslim world
. One of the earliest of these was Al-Kindi
(c. 801–73). In 984, the Persian mathematician Ibn Sahl
wrote the treatise "On burning mirrors and lenses", correctly describing a law of refraction equivalent to Snell's law. He used this law to compute optimum shapes for lenses and curved mirror
s. In the early 11th century, Alhazen (Ibn al-Haytham) wrote his Book of Optics
, which documented the then-current understanding of vision.
In the 13th century, Roger Bacon
used parts of glass spheres as magnifying glass
es, and discovered that light reflects from objects rather than being released from them. In Italy, around 1284, Salvino D'Armate
invented the first wearable eyeglasses.
The earliest known telescopes were refracting telescope
s developed within the Netherlands
eyeglass industry in 1608 with contemporaneous or after the fact claims of invention citing three individuals: Hans Lippershey
and Zacharias Janssen
, who were spectacle makers in Middelburg
, and Jacob Metius
of Alkmaar
. In Italy, Galileo
greatly improved upon these designs the following year. In 1668, Isaac Newton
constructed the first practical reflecting telescope
, which bears his name, the Newtonian reflector
.
The first microscope was made around 1595, also in Middelburg. Three different eyeglass makers have been given credit for the invention: Lippershey, Janssen, and his father, Hans. The coining of the name "microscope" has been credited to Giovanni Faber
, who gave that name to Galileo's compound microscope in 1625.
Optical theory progressed in the mid-17th century with treatises written by philosopher René Descartes
, which explained a variety of optical phenomena including reflection and refraction by assuming that light was emitted by objects which produced it. This differed substantively from the ancient Greek emission theory. In the late 1660s and early 1670s, Newton expanded Descartes' ideas into a corpuscle theory of light, famously showing that white light, instead of being a unique color, was really a composite of different colors that can be separated into a spectrum
with a prism
. In 1690, Christian Huygens proposed a wave theory for light based on suggestions that had been made by Robert Hooke
in 1664. Hooke himself publicly criticized Newton's theories of light and the feud between the two lasted until Hooke's death. In 1704, Newton published Opticks
and, at the time, partly because of his success in other areas of physics
, he was generally considered to be the victor in the debate over the nature of light.
Newtonian optics was generally accepted until the early 19th century when Thomas Young
and Augustin-Jean Fresnel
conducted experiments on the interference of light that firmly established light's wave nature. Young's famous double slit experiment
showed that light followed the law of superposition
, which is a wave-like property not predicted by Newton's corpuscle theory. This work led to a theory of diffraction for light and opened an entire area of study in physical optics. Wave optics was successfully unified with electromagnetic theory by James Clerk Maxwell
in the 1860s.
The next development in optical theory came in 1899 when Max Planck
correctly modeled blackbody radiation by assuming that the exchange of energy between light and matter only occurred in discrete amounts he called quanta. In 1905, Albert Einstein
published the theory of the photoelectric effect
that firmly established the quantization of light itself. In 1913, Niels Bohr
showed that atoms could only emit discrete amounts of energy, thus explaining the discrete lines seen in emission
and absorption spectra. The understanding of the interaction between light and matter, which followed from these developments, not only formed the basis of quantum optics but also was crucial for the development
of quantum mechanics
as a whole. The ultimate culmination was the theory of quantum electrodynamics
, which explains all optics and electromagnetic processes in general as being the result of the exchange of real and virtual photon
s.
Quantum optics gained practical importance with the invention of the maser
in 1953 and the laser in 1960. Following the work of Paul Dirac
in quantum field theory
, George Sudarshan
, Roy J. Glauber
, and Leonard Mandel
applied quantum theory to the electromagnetic field in the 1950s and 1960s to gain a more detailed understanding of photodetection and the statistics
of light.
Geometrical optics can be viewed as an approximation of physical optics which can be applied when the wavelength of the light used is much smaller than the size of the optical elements or system being modelled.
of light in terms of "rays" which travel in straight lines, and whose paths are governed by the laws of reflection and refraction at interfaces between different media. These laws were discovered empirically as far back as 984AD and have been used in the design of optical components and instruments from then until the present day. They can be summarised as follows:
When a ray of light hits the boundary between two transparent materials, it is divided into a reflected and a refracted ray.
where is a constant for any two materials and a given colour of light. It is known as the refractive index
.
The laws of reflection and refraction can be derived from Fermat's principle
which states that the path taken between two points by a ray of light is the path that can be traversed in the least time.
, or "small angle approximation." The mathematical behavior then becomes linear, allowing optical components and systems to be described by simple matrices. This leads to the techniques of Gaussian optics
and paraxial ray tracing
, which are used to find basic properties of optical systems, such as approximate image
and object positions and magnification
s.
Reflections can be divided into two types: specular reflection
and diffuse reflection
. Specular reflection describes the gloss of surfaces such as mirrors, which reflect light in a simple, predictable way. This allows for production of reflected images that can be associated with an actual (real
) or extrapolated (virtual
) location in space. Diffuse reflection describes opaque, non limpid materials, such as paper or rock. The reflections from these surfaces can only be described statistically, with the exact distribution of the reflected light depending on the microscopic structure of the material. Many diffuse reflectors are described or can be approximated by Lambert's cosine law
, which describes surfaces that have equal luminance
when viewed from any angle. Glossy surfaces can give both specular and diffuse reflection.
In specular reflection, the direction of the reflected ray is determined by the angle the incident ray makes with the surface normal
, a line perpendicular to the surface at the point where the ray hits. The incident and reflected rays and the normal lie in a single plane, and the angle between the reflected ray and the surface normal is the same as that between the incident ray and the normal. This is known as the Law of Reflection.
For flat mirrors
, the law of reflection implies that images of objects are upright and the same distance behind the mirror as the objects are in front of the mirror. The image size is the same as the object size. The law also implies that mirror image
s are parity inverted
, which we perceive as a left-right inversion. Images formed from reflection in two (or any even number of) mirrors are not parity inverted. Corner reflector
s retroreflect
light, producing reflected rays that travel back in the direction from which the incident rays came.
Mirrors with curved surfaces
can be modeled by ray-tracing
and using the law of reflection at each point on the surface. For mirrors with parabolic surfaces
, parallel rays incident on the mirror produce reflected rays that converge at a common focus
. Other curved surfaces may also focus light, but with aberrations due to the diverging shape causing the focus to be smeared out in space. In particular, spherical mirrors exhibit spherical aberration
. Curved mirrors can form images with magnification greater than or less than one, and the magnification can be negative, indicating that the image is inverted. An upright image formed by reflection in a mirror is always virtual, while an inverted image is real and can be projected onto a screen.
Refraction occurs when light travels through an area of space that has a changing index of refraction; this principle allows for lenses and the focusing of light. The simplest case of refraction occurs when there is an interface between a uniform medium with index of refraction 
and another medium with index of refraction 
. In such situations, Snell's Law
describes the resulting deflection of the light ray:
where
and 
are the angles between the normal (to the interface) and the incident and refracted waves, respectively. This phenomenon is also associated with a changing speed of light as seen from the definition of index of refraction provided above which implies:
where
and 
are the wave velocities through the respective media.
Various consequences of Snell's Law include the fact that for light rays traveling from a material with a high index of refraction to a material with a low index of refraction, it is possible for the interaction with the interface to result in zero transmission. This phenomenon is called total internal reflection
and allows for fiber optics technology. As light signals travel down a fiber optic cable, it undergoes total internal reflection allowing for essentially no light lost over the length of the cable. It is also possible to produce polarized light rays using a combination of reflection and refraction: When a refracted ray and the reflected ray form a right angle
, the reflected ray has the property of "plane polarization". The angle of incidence required for such a scenario is known as Brewster's angle.
Snell's Law can be used to predict the deflection of light rays as they pass through "linear media" as long as the indexes of refraction and the geometry of the media are known. For example, the propagation of light through a prism results in the light ray being deflected depending on the shape and orientation of the prism. Additionally, since different frequencies of light have slightly different indexes of refraction in most materials, refraction can be used to produce dispersion spectra that appear as rainbows. The discovery of this phenomenon when passing light through a prism is famously attributed to Isaac Newton.
Some media have an index of refraction which varies gradually with position and, thus, light rays curve through the medium rather than travel in straight lines. This effect is what is responsible for mirage
s seen on hot days where the changing index of refraction of the air causes the light rays to bend creating the appearance of specular reflections in the distance (as if on the surface of a pool of water). Material that has a varying index of refraction is called a gradient-index (GRIN) material and has many useful properties used in modern optical scanning technologies including photocopiers and scanners
. The phenomenon is studied in the field of gradient-index optics.
A device which produces converging or diverging light rays due to refraction is known as a lens. Thin lenses produce focal points on either side that can be modeled using the lensmaker's equation. In general, two types of lenses exist: convex lenses, which cause parallel light rays to converge, and concave lenses, which cause parallel light rays to diverge. The detailed prediction of how images are produced by these lenses can be made using ray-tracing similar to curved mirrors. Similarly to curved mirrors, thin lenses follow a simple equation that determines the location of the images given a particular focal length (
) and object distance (
):
where
is the distance associated with the image and is considered by convention to be negative if on the same side of the lens as the object and positive if on the opposite side of the lens. The focal length f is considered negative for concave lenses.
Incoming parallel rays are focused by a convex lens into an inverted real image one focal length from the lens, on the far side of the lens. Rays from an object at finite distance are focused further from the lens than the focal distance; the closer the object is to the lens, the further the image is from the lens. With concave lenses, incoming parallel rays diverge after going through the lens, in such a way that they seem to have originated at an upright virtual image one focal length from the lens, on the same side of the lens that the parallel rays are approaching on. Rays from an object at finite distance are associated with a virtual image that is closer to the lens than the focal length, and on the same side of the lens as the object. The closer the object is to the lens, the closer the virtual image is to the lens.
Likewise, the magnification of a lens is given by
where the negative sign is given, by convention, to indicate an upright object for positive values and an inverted object for negative values. Similar to mirrors, upright images produced by single lenses are virtual while inverted images are real.
Lenses suffer from aberrations that distort images and focal points. These are due to both to geometrical imperfections and due to the changing index of refraction for different wavelengths of light (chromatic aberration
).
. This model predicts phenomena such as interference and diffraction
which are not explained by geometric optics. The speed of light
waves is approximately 3.10 8 m/s. The wavelength
of visible light waves varies between 400-700nm but light waves are usually considered to also include infrared
waves (0.7-300μm) and ultraviolet waves (10-400nm).
The wave model can be used to make predictions about how an optical system will behave without requiring an explanation of what is "waving" in what medium. Until the middle of the 19th century, most physicists believed in an "ethereal" medium in which the light disturbance propagated. The existence of electromagnetic waves was predicted in 1865 by Maxwell's equations. These waves propagate at the speed of light
and have varying electric and magnetic fields which are orthogonal to one another, and also to the direction of propagation of the waves. Light waves are now generally treated as electromagnetic waves except when quantum mechanical effects have to be considered.
quantity to represent the electric field of the light wave, rather than using a vector
model with orthogonal electric and magnetic vectors.
The Huygens–Fresnel equation is one such model. This was derived empirically by Fresnel in 1815, based on Huygen's hypothesis that each point on a wavefront generates a secondary spherical wavefront, which Fresnel combined with the principle of superposition
of waves. The Kirchoff diffraction equation
, which is derived using Maxwell's equations, puts the Huygens-Fresnel equation on a firmer physical foundation. Examples of the application of Huygens–Fresnel principle can be found in the sections on diffraction
and Fraunhofer diffraction
.
More rigorous models, involving the modelling of both electric and magnetic fields of the light wave, are required when dealing with the detailed interaction of light with materials where the interaction depends on their electric and magnetic properties. For instance, the behaviour of a light wave interacting with a metal surface is quite different from what happens when it interacts with a di-electric material. A vector model must also be used to model polarized light.
Numerical modeling
techniques such as the Finite element method
, the Boundary element method
and the Transmission-line matrix method can be used to model the propagation of light in systems which cannot be solved analytically. Such models are computationally demanding and are normally only used to solve small-scale problems that require accuracy beyond that which can be achieved with analytical solutions.
All of the results from geometrical optics can be recovered using the techniques of Fourier optics
which apply many of the same mathematical and analytical techniques used in acoustic engineering and signal processing
.
Gaussian beam propagation
is a simple paraxial physical optics model for the propagation of coherent radiation such as laser beams. This technique partially accounts for diffraction, allowing accurate calculations of the rate at which a laser beam expands with distance, and the minimum size to which the beam can be focused. Gaussian beam propagation thus bridges the gap between geometric and physical optics.
effects, the superposition principle
can be used to predict the shape of interacting waveforms through the simple addition of the disturbances. This interaction of waves to produce a resulting pattern is generally termed "interference" and can result in a variety of outcomes. If two waves of the same wavelength and frequency are in phase
, both the wave crests and wave troughs align. This results in constructive interference and an increase in the amplitude of the wave, which for light is associated with a brightening of the waveform in that location. Alternatively, if the two waves of the same wavelength and frequency are out of phase, then the wave crests will align with wave troughs and vice-versa. This results in destructive interference and a decrease in the amplitude of the wave, which for light is associated with a dimming of the waveform at that location. See below for an illustration of this effect.
Since the Huygens–Fresnel principle states that every point of a wavefront is associated with the production of a new disturbance, it is possible for a wavefront to interfere with itself constructively or destructively at different locations producing bright and dark fringes in regular and predictable patterns. Interferometry
is the science of measuring these patterns, usually as a means of making precise determinations of distances or angular resolution
s. The Michelson interferometer
was a famous instrument which used interference effects to accurately measure the speed of light.
The appearance of thin films and coatings is directly affected by interference effects. Antireflective coatings use destructive interference to reduce the reflectivity of the surfaces they coat, and can be used to minimize glare and unwanted reflections. The simplest case is a single layer with thickness one-fourth the wavelength of incident light. The reflected wave from the top of the film and the reflected wave from the film/material interface are then exactly 180° out of phase, causing destructive interference. The waves are only exactly out of phase for one wavelength, which would typically be chosen to be near the center of the visible spectrum, around 550 nm. More complex designs using multiple layers can achieve low reflectivity over a broad band, or extremely low reflectivity at a single wavelength.
Constructive interference in thin films can create strong reflection of light in a range of wavelengths, which can be narrow or broad depending on the design of the coating. These films are used to make dielectric mirror
s, interference filter
s, heat reflectors, and filters for color separation in color television
cameras. This interference effect is also what causes the colorful rainbow patterns seen in oil slicks.
, who also coined the term from the Latin diffringere, 'to break into pieces'. Later that century, Robert Hooke and Isaac Newton also described phenomena now known to be diffraction in Newton's rings
while James Gregory
recorded his observations of diffraction patterns from bird feathers.
The first physical optics model of diffraction that relied on the Huygens–Fresnel principle was developed in 1803 by Thomas Young
in his interference experiments
with the interference patterns of two closely spaced slits. Young showed that his results could only be explained if the two slits acted as two unique sources of waves rather than corpuscles. In 1815 and 1818, Augustin-Jean Fresnel firmly established the mathematics of how wave interference can account for diffraction.
The simplest physical models of diffraction use equations that describe the angular separation of light and dark fringes due to light of a particular wavelength (
). In general, the equation takes the form
where
is the separation between two wavefront sources (in the case of Young's experiments, it was two slits
),
is the angular separation between the central fringe and the 
th order fringe, where the central maximum is 
.
This equation is modified slightly to take into account a variety of situations such as diffraction through a single gap, diffraction through multiple slits, or diffraction through a diffraction grating
that contains a large number of slits at equal spacing. More complicated models of diffraction require working with the mathematics of Fresnel
or Fraunhofer diffraction
.
X-ray diffraction makes use of the fact that atoms in a crystal
have regular spacing at distances that are on the order of one angstrom
. To see diffraction patterns, x-rays with similar wavelengths to that spacing are passed through the crystal. Since crystals are three-dimensional objects rather than two-dimensional gratings, the associated diffraction pattern varies in two directions according to Bragg reflection, with the associated bright spots occurring in unique patterns
and
being twice the spacing between atoms.
Diffraction effects limit the ability for an optical detector to optically resolve
separate light sources. In general, light that is passing through an aperture
will experience diffraction and the best images that can be created (as described in diffraction-limited optics) appear as a central spot with surrounding bright rings, separated by dark nulls; this pattern is known as an Airy pattern, and the central bright lobe as an Airy disk. The size of such a disk is given by
where θ is the angular resolution, λ is the wavelength
of the light, and D is the diameter
of the lens aperture. If the angular separation of the two points is significantly less than the Airy disk angular radius, then the two points cannot be resolved in the image, but if their angular separation is much greater than this, distinct images of the two points are formed and they can therefore be resolved. Rayleigh
defined the somewhat arbitrary "Rayleigh criterion" that two points whose angular separation is equal to the Airy disk radius (measured to first null, that is, to the first place where no light is seen) can be considered to be resolved. It can be seen that the greater the diameter of the lens or its aperture, the finer the resolution. Interferometry, with its ability to mimic extremely large baseline apertures, allows for the greatest angular resolution possible.
For astronomical imaging, the atmosphere prevents optimal resolution from being achieved in the visible spectrum due to the atmospheric scattering
and dispersion which cause stars to twinkle
. Astronomers refer to this effect as the quality of astronomical seeing
. Techniques known as adaptive optics
have been utilized to eliminate the atmospheric disruption of images and achieve results that approach the diffraction limit.
Refractive processes take place in the physical optics limit, where the wavelength of light is similar to other distances, as a kind of scattering. The simplest type of scattering is Thomson scattering
which occurs when electromagnetic waves are deflected by single particles. In the limit of Thompson scattering, in which the wavelike nature of light is evident, light is dispersed independent of the frequency, in contrast to Compton scattering
which is frequency-dependent and strictly a quantum mechanical process, involving the nature of light as particles. In a statistical sense, elastic scattering of light by numerous particles much smaller than the wavelength of the light is a process known as Rayleigh scattering
while the similar process for scattering by particles that are similar or larger in wavelength is known as Mie scattering with the Tyndall effect
being a commonly observed result. A small proportion of light scattering from atoms or molecules may undergo Raman scattering
, wherein the frequency changes due to excitation of the atoms and molecules. Brillouin scattering
occurs when the frequency of light changes due to local changes with time and movements of a dense material.
Dispersion occurs when different frequencies of light have different phase velocities
, due either to material properties (material dispersion) or to the geometry of an optical waveguide (waveguide dispersion). The most familiar form of dispersion is a decrease in index of refraction with increasing wavelength, which is seen in most transparent materials. This is called "normal dispersion". It occurs in all dielectric materials
, in wavelength ranges where the material does not absorb light. In wavelength ranges where a medium has significant absorption, the index of refraction can increase with wavelength. This is called "anomalous dispersion".
The separation of colors by a prism is an example of normal dispersion. At the surfaces of the prism, Snell's law predicts that light incident at an angle θ to the normal will be refracted at an angle arcsin(sin (θ) / n) . Thus, blue light, with its higher refractive index, is bent more strongly than red light, resulting in the well-known rainbow
pattern.
Material dispersion is often characterized by the Abbe number
, which gives a simple measure of dispersion based on the index of refraction at three specific wavelengths. Waveguide dispersion is dependent on the propagation constant
. Both kinds of dispersion cause changes in the group characteristics of the wave, the features of the wave packet that change with the same frequency as the amplitude of the electromagnetic wave. "Group velocity dispersion" manifests as a spreading-out of the signal "envelope" of the radiation and can be quantified with a group dispersion delay parameter:
where
is the group velocity. For a uniform medium, the group velocity is
where n is the index of refraction and c is the speed of light in a vacuum. This gives a simpler form for the dispersion delay parameter:
If D is less than zero, the medium is said to have positive dispersion or normal dispersion. If D is greater than zero, the medium has negative dispersion. If a light pulse is propagated through a normally dispersive medium, the result is the higher frequency components slow down more than the lower frequency components. The pulse therefore becomes positively chirp
ed, or up-chirped, increasing in frequency with time. This causes the spectrum coming out of a prism to appear with red light the least refracted and blue/violet light the most refracted. Conversely, if a pulse travels through an anomalously (negatively) dispersive medium, high frequency components travel faster than the lower ones, and the pulse becomes negatively chirped, or down-chirped, decreasing in frequency with time.
The result of group velocity dispersion, whether negative or positive, is ultimately temporal spreading of the pulse. This makes dispersion management extremely important in optical communications systems based on optical fiber
s, since if dispersion is too high, a group of pulses representing information will each spread in time and merge together, making it impossible to extract the signal.
s such as many electromagnetic waves, it describes the orientation of the oscillations in the plane perpendicular to the wave's direction of travel. The oscillations may be oriented in a single direction (linear polarization
), or the oscillation direction may rotate as the wave travels (circular
or elliptical polarization
). Circularly polarized waves can rotate rightward or leftward in the direction of travel, and which of those two rotations is present in a wave is called the wave's chirality
.
The typical way to consider polarization is to keep track of the orientation of the electric field vector as the electromagnetic wave propagates. The electric field vector of a plane wave may be arbitrarily divided into two perpendicular components labeled x and y (with z indicating the direction of travel). The shape traced out in the x-y plane by the electric field vector is a Lissajous figure
that describes the polarization state. The following figures show some examples of the evolution of the electric field vector (blue), with time (the vertical axes), at a particular point in space, along with its x and y components (red/left and green/right), and the path traced by the vector in the plane (purple): The same evolution would occur when looking at the electric field at a particular time while evolving the point in space, along the direction opposite to propagation.
In the leftmost figure above, the x and y components of the light wave are in phase. In this case, the ratio of their strengths is constant, so the direction of the electric vector (the vector sum of these two components) is constant. Since the tip of the vector traces out a single line in the plane, this special case is called linear polarization
. The direction of this line depends on the relative amplitudes of the two components.
In the middle figure, the two orthogonal components have the same amplitudes and are 90° out of phase. In this case, one component is zero when the other component is at maximum or minimum amplitude. There are two possible phase relationships that satisfy this requirement: the x component can be 90° ahead of the y component or it can be 90° behind the y component. In this special case, the electric vector traces out a circle in the plane, so this polarization is called circular polarization. The rotation direction in the circle depends on which of the two phase relationships exists and corresponds to right-hand circular polarization and left-hand circular polarization.
In all other cases, where the two components either do not have the same amplitudes and/or their phase difference is neither zero nor a multiple of 90°, the polarization is called elliptical polarization
because the electric vector traces out an ellipse
in the plane (the polarization ellipse). This is shown in the above figure on the right. Detailed mathematics of polarization is done using Jones calculus
and is characterized by the Stokes parameters
.
Media that have different indexes of refraction for different polarization modes are called birefringent
. Well known manifestations of this effect appear in optical wave plate
s/retarders (linear modes) and in Faraday rotation/optical rotation
(circular modes). If the path length in the birefringent medium is sufficient, plane waves will exit the material with a significantly different propagation direction, due to refraction
. For example, this is the case with macroscopic crystals of calcite
, which present the viewer with two offset, orthogonally polarized images of whatever is viewed through them. It was this effect that provided the first discovery of polarization, by Erasmus Bartholinus in 1669. In addition, the phase shift, and thus the change in polarization state, is usually frequency dependent, which, in combination with dichroism
, often gives rise to bright colors and rainbow-like effects. In mineralogy
, such properties, known as pleochroism
, are frequently exploited for the purpose of identifying minerals using polarization microscope
s. Additionally, many plastics that are not normally birefringent will become so when subject to mechanical stress, a phenomenon which is the basis of photoelasticity
. Non-birefringent methods, to rotate the linear polarization of light beams, include the use of prismatic polarization rotator
s which utilize total internal reflection
in a prism set designed for efficient colinear transmission.
Media that reduce the amplitude of certain polarization modes are called dichroic
. with devices that block nearly all of the radiation in one mode known as polarizing filters or simply "polarizer
s". Malus' law, which is named after Etienne-Louis Malus
, says that when a perfect polarizer is placed in a linear polarized beam of light, the intensity, I, of the light that passes through is given by
where
A beam of unpolarized light can be thought of as containing a uniform mixture of linear polarizations at all possible angles. Since the average value of
is 1/2, the transmission coefficient becomes
In practice, some light is lost in the polarizer and the actual transmission of unpolarized light will be somewhat lower than this, around 38% for Polaroid-type polarizers but considerably higher (>49.9%) for some birefringent prism types.
In addition to birefringence and dichroism in extended media, polarization effects can also occur at the (reflective) interface between two materials of different refractive index. These effects are treated by the Fresnel equations
. Part of the wave is transmitted and part is reflected, with the ratio depending on angle of incidence and the angle of refraction. In this way, physical optics recovers Brewster's angle
.
Most sources of electromagnetic radiation
contain a large number of atoms or molecules that emit light. The orientation of the electric fields produced by these emitters may not be correlated, in which case the light is said to be unpolarized. If there is partial correlation between the emitters, the light is partially polarized. If the polarization is consistent across the spectrum of the source, partially polarized light can be described as a superposition of a completely unpolarized component, and a completely polarized one. One may then describe the light in terms of the degree of polarization
, and the parameters of the polarization ellipse.
Light reflected by shiny transparent materials is partly or fully polarized, except when the light is normal (perpendicular) to the surface. It was this effect that allowed the mathematician Etienne Louis Malus to make the measurements that allowed for his development of the first mathematical models for polarized light. Polarization occurs when light is scattered in the atmosphere
. The scattered light produces the brightness and color in clear skies
. This partial polarization of scattered light can be taken advantage of using polarizing filters to darken the sky in photographs
. Optical polarization is principally of importance in chemistry
due to circular dichroism
and optical rotation
("circular birefringence") exhibited by optically active (chiral
) molecules.
, deals with specifically quantum mechanical properties of light. Quantum optics is not just theoretical; some modern devices, such as lasers, have principles of operation that depend on quantum mechanics. Light detectors, such as photomultiplier
s and channeltrons, respond to individual photons. Electronic image sensor
s, such as CCDs
, exhibit shot noise
corresponding to the statistics of individual photon events. Light-emitting diode
s and photovoltaic cells, too, cannot be understood without quantum mechanics. In the study of these devices, quantum optics often overlaps with quantum electronics.
Specialty areas of optics research include the study of how light interacts with specific materials as in crystal optics
and metamaterial
s. Other research focuses on the phenomenology of electromagnetic waves as in singular optics
, non-imaging optics, non-linear optics, statistical optics, and radiometry
. Additionally, computer engineers have taken an interest in integrated optics, machine vision
, and photonic computing
as possible components of the "next generation" of computers.
Today, the pure science of optics is called optical science or optical physics
to distinguish it from applied optical sciences, which are referred to as optical engineering
. Prominent subfields of optical engineering include illumination engineering
, photonics
, and optoelectronics
with practical applications like lens design
, fabrication and testing of optical components
, and image processing
. Some of these fields overlap, with nebulous boundaries between the subjects terms that mean slightly different things in different parts of the world and in different areas of industry. A professional community of researchers in nonlinear optics has developed in the last several decades due to advances in laser technology
.
A laser is a device that emits light (electromagnetic radiation) through a process called stimulated emission
. The term laser is an acronym for Light Amplification by Stimulated Emission of Radiation. Laser light is usually spatially coherent
, which means that the light either is emitted in a narrow, low-divergence beam
, or can be converted into one with the help of optical components such as lens
es. Because the microwave
equivalent of the laser, the maser, was developed first, devices that emit microwave and radio
frequencies are usually called masers.
The first working laser was demonstrated on 16 May 1960 by Theodore Maiman at Hughes Research Laboratories
. When first invented, they were called "a solution looking for a problem". Since then, lasers have become a multi-billion dollar industry, finding utility in thousands of highly varied applications. The first application of lasers visible in the daily lives of the general population was the supermarket barcode
scanner, introduced in 1974. The laserdisc
player, introduced in 1978, was the first successful consumer product to include a laser, but the compact disc
player was the first laser-equipped device to become truly common in consumers' homes, beginning in 1982. These optical storage
devices use a semiconductor laser less than a millimeter wide to scan the surface of the disc for data retrieval. Fiber-optic communication
relies on lasers to transmit large amounts of information at the speed of light. Other common applications of lasers include laser printers and laser pointer
s. Lasers are used in medicine in areas such as bloodless surgery
, laser eye surgery, and laser capture microdissection
and in military applications such as missile defense systems, electro-optical countermeasures (EOCM), and LIDAR
. Lasers are also used in holograms, bubblegram
s, laser light shows
, and laser hair removal
.
s in biology indicate the central role optics plays as the science of one of the five senses
. Many people benefit from eyeglasses or contact lenses, and optics are integral to the functioning of many consumer goods including cameras. Rainbows and mirage
s are examples of optical phenomena. Optical communication
provides the backbone for both the Internet
and modern telephony
.
The human eye functions by focusing light onto an array of photoreceptor cells called the retina
, which covers the back of the eye. The focusing is accomplished by a series of transparent media. Light entering the eye passes first through the cornea
, which provides much of the eye's optical power. The light then continues through the fluid just behind the cornea—the anterior chamber
, then passes through the pupil
. The light then passes through the lens
, which focuses the light further and allows adjustment of focus. The light then passes through the main body of fluid in the eye—the vitreous humor, and reaches the retina. The cells in the retina cover the back of the eye, except for where the optic nerve
exits; this results in a blind spot
.
There are two types of photoreceptor cells, rods and cones, which are sensitive to different aspects of light. Rod cells are sensitive to the intensity of light over a wide frequency range, thus are responsible for black-and-white vision
. Rod cells are not present on the fovea
, the area of the retina responsible for central vision, and are not as responsive as cone cells to spatial and temporal changes in light. There are, however, twenty times more rod cells than cone cells in the retina because the rod cells are present across a wider area. Because of their wider distribution, rods are responsible for peripheral vision
.
In contrast, cone cells are less sensitive to the overall intensity of light, but come in three varieties that are sensitive to different frequency-ranges and thus are used in the perception of color
and photopic vision
. Cone cells are highly concentrated in the fovea and have a high visual acuity meaning that they are better at spatial resolution than rod cells. Since cone cells are not as sensitive to dim light as rod cells, most night vision
is limited to rod cells. Likewise, since cone cells are in the fovea, central vision (including the vision needed to do most reading, fine detail work such as sewing, or careful examination of objects) is done by cone cells.
Ciliary muscle
s around the lens allow the eye's focus to be adjusted. This process is known as accommodation
. The near point and far point
define the nearest and farthest distances from the eye at which an object can be brought into sharp focus. For a person with normal vision, the far point is located at infinity. The near point's location depends on how much the muscles can increase the curvature of the lens, and how inflexible the lens has become with age. Optometrists, ophthalmologists, and optician
s usually consider an appropriate near point to be closer than normal reading distance—approximately 25 cm.
Defects in vision can be explained using optical principles. As people age, the lens becomes less flexible and the near point recedes from the eye, a condition known as presbyopia
. Similarly, people suffering from hyperopia
cannot decrease the focal length of their lens enough to allow for nearby objects to be imaged on their retina. Conversely, people who cannot increase the focal length of their lens enough to allow for distant objects to be imaged on the retina suffer from myopia
and have a far point that is considerably closer than infinity. A condition known as astigmatism
results when the cornea is not spherical but instead is more curved in one direction. This causes horizontally extended objects to be focused on different parts of the retina than vertically extended objects, and results in distorted images.
All of these conditions can be corrected using corrective lens
es. For presbyopia and hyperopia, a converging lens provides the extra curvature necessary to bring the near point closer to the eye while for myopia a diverging lens provides the curvature necessary to send the far point to infinity. Astigmatism is corrected with a cylindrical surface
lens that curves more strongly in one direction than in another, compensating for the non-uniformity of the cornea.
The optical power of corrective lenses is measured in diopters, a value equal to the reciprocal
of the focal length measured in meters; with a positive focal length corresponding to a converging lens and a negative focal length corresponding to a diverging lens. For lenses that correct for astigmatism as well, three numbers are given: one for the spherical power, one for the cylindrical power, and one for the angle of orientation of the astigmatism.
Optical illusions (also called visual illusions) are characterized by visually perceived
images that differ from objective reality. The information gathered by the eye is processed in the brain to give a percept that differs from the object being imaged. Optical illusions can be the result of a variety of phenomena including physical effects that create images that are different from the objects that make them, the physiological effects on the eyes and brain of excessive stimulation (e.g. brightness, tilt, color, movement), and cognitive illusions where the eye and brain make unconscious inferences.
Cognitive illusions include some which result from the unconscious misapplication of certain optical principles. For example, the Ames room
, Hering
, Müller-Lyer, Orbison, Ponzo
, Sander
, and Wundt illusion
s all rely on the suggestion of the appearance of distance by using converging and diverging lines, in the same way that parallel light rays (or indeed any set of parallel lines) appear to converge at a vanishing point
at infinity in two-dimensionally rendered images with artistic perspective
. This suggestion is also responsible for the famous moon illusion
where the moon, despite having essentially the same angular size, appears much larger near the horizon
than it does at zenith
. This illusion so confounded Ptolemy that he incorrectly attributed it to atmospheric refraction when he described it in his treatise, Optics.
Another type of optical illusion exploits broken patterns to trick the mind into perceiving symmetries or asymmetries that are not present. Examples include the café wall
, Ehrenstein
, Fraser spiral
, Poggendorff
, and Zöllner illusion
s. Related, but not strictly illusions, are patterns that occur due to the superimposition of periodic structures. For example transparent tissues with a grid structure produce shapes known as moiré pattern
s, while the superimposition of periodic transparent patterns comprising parallel opaque lines or curves produces line moiré
patterns.
Single lenses have a variety of applications including photographic lens
es, corrective lenses, and magnifying glass
es while single mirrors are used in parabolic reflector
s and rear-view mirror
s. Combining a number of mirrors, prisms, and lenses produces compound optical instruments which have practical uses. For example, a periscope
is simply two plane mirrors aligned to allow for viewing around obstructions. The most famous compound optical instruments in science are the microscope
and the telescope
which were both invented by the Dutch in the late 16th century.
Microscopes were first developed with just two lenses: an objective lens and an eyepiece
. The objective lens is essentially a magnifying glass and was designed with a very small focal length while the eyepiece generally has a longer focal length. This has the effect of producing magnified images of close objects. Generally, an additional source of illumination is used since magnified images are dimmer due to the conservation of energy
and the spreading of light rays over a larger surface area. Modern microscopes, known as compound microscopes have many lenses in them (typically four) to optimize the functionality and enhance image stability. A slightly different variety of microscope, the comparison microscope
, looks at side-by-side images to produce a stereoscopic binocular
view that appears three dimensional when used by humans.
The first telescopes, called refracting telescope
s were also developed with a single objective and eyepiece lens. In contrast to the microscope, the objective lens of the telescope was designed with a large focal length to avoid optical aberrations. The objective focuses an image of a distant object at its focal point which is adjusted to be at the focal point of an eyepiece of a much smaller focal length. The main goal of a telescope is not necessarily magnification, but rather collection of light which is determined by the physical size of the objective lens. Thus, telescopes are normally indicated by the diameters of their objectives rather than by the magnification which can be changed by switching eyepieces. Because the magnification of a telescope is equal to the focal length of the objective divided by the focal length of the eyepiece, smaller focal-length eyepieces cause greater magnification.
Since crafting large lenses is much more difficult than crafting large mirrors, most modern telescopes are reflecting telescope
s, that is, telescopes that use a primary mirror rather than an objective lens. The same general optical considerations apply to reflecting telescopes that applied to refracting telescopes, namely, the larger the primary mirror, the more light collected, and the magnification is still equal to the focal length of the primary mirror divided by the focal length of the eyepiece. Professional telescopes generally do not have eyepieces and instead place an instrument (often a charge-coupled device) at the focal point instead.
The optics of photography
involves both lenses
and the medium in which the electromagnetic radiation is recorded, whether it be a plate, film
, or charge-coupled device
. Photographers must consider the reciprocity
of the camera and the shot which is summarized by the relation
In other words, the smaller the aperture (giving greater depth of focus), the less light coming in, so the length of time has to be increased (leading to possible blurriness if motion occurs). An example of the use of the law of reciprocity is the Sunny 16 rule
which gives a rough estimate for the settings needed to estimate the proper exposure
in daylight.
A camera's aperture is measured by a unitless number called the f-number
or f-stop, #, often notated as
, and given by
where
is the focal length
, and
is the diameter of the entrance pupil. By convention, "#" is treated as a single symbol, and specific values of # are written by replacing the number sign
with the value. The two ways to increase the f-stop are to either decrease the diameter of the entrance pupil or change to a longer focal length (in the case of a zoom lens
, this can be done by simply adjusting the lens). Higher f-numbers also have a larger depth of field
due to the lens approaching the limit of a pinhole camera
which is able to focus all images perfectly, regardless of distance, but requires very long exposure times.
The field of view that the lens will provide changes with the focal length of the lens. There are three basic classifications based on the relationship to the diagonal size of the film or sensor size of the camera to the focal length of the lens:
Modern zoom lens
es may have some or all of these attributes.
The absolute value for the exposure time required depends on how sensitive
to light the medium being used is (measured by the film speed
, or, for digital media, by the quantum efficiency
). Early photography used media that had very low light sensitivity, and so exposure times had to be long even for very bright shots. As technology has improved, so has the sensitivity through film cameras and digital cameras.
Other results from physical and geometrical optics apply to camera optics. For example, the maximum resolution capability of a particular camera set-up is determined by the diffraction limit associated with the pupil size and given, roughly, by the Rayleigh criterion.
The unique optical properties of the atmosphere cause a wide range of spectacular optical phenomena. The blue color of the sky is a direct result of Rayleigh scattering
which redirects higher frequency (blue) sunlight back into the field of view of the observer. Because blue light is scattered more easily than red light, the sun takes on a reddish hue when it is observed through a thick atmosphere, as during a sunrise
or sunset
. Additional particulate matter in the sky can scatter different colors at different angles creating colorful glowing skies at dusk and dawn. Scattering off of ice crystals and other particles in the atmosphere are responsible for halos
, afterglow
s, coronas
, rays of sunlight
, and sun dog
s. The variation in these kinds of phenomena is due to different particle sizes and geometries.
Mirage
s are optical phenomena in which light rays are bent due to thermal variations in the refraction index of air, producing displaced or heavily distorted images of distant objects. Other dramatic optical phenomena associated with this include the Novaya Zemlya effect
where the sun appears to rise earlier than predicted with a distorted shape. A spectacular form of refraction occurs with a temperature inversion
called the Fata Morgana
where objects on the horizon or even beyond the horizon, such as islands, cliffs, ships or icebergs, appear elongated and elevated, like "fairy tale castles".
Rainbow
s are the result of a combination of internal reflection and dispersive refraction of light in raindrops. A single reflection off the backs of an array of raindrops produces a rainbow with an angular size on the sky that ranges from 40° to 42° with red on the outside. Double rainbows are produced by two internal reflections with angular size of 50.5° to 54° with violet on the outside. Because rainbows are seen with the sun 180° away from the center of the rainbow, rainbows are more prominent the closer the sun is to the horizon.
Textbooks and tutorials
Wikibooks modules
Further reading
Societies
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
which involves the behavior and properties of light
Light
Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...
, including its interactions with matter
Matter
Matter is a general term for the substance of which all physical objects consist. Typically, matter includes atoms and other particles which have mass. A common way of defining matter is as anything that has mass and occupies volume...
and the construction of instruments that use or detect
Photodetector
Photosensors or photodetectors are sensors of light or other electromagnetic energy. There are several varieties:*Active pixel sensors are image sensors consisting of an integrated circuit that contains an array of pixel sensors, each pixel containing a both a light sensor and an active amplifier...
it. Optics usually describes the behavior of visible, ultraviolet
Ultraviolet
Ultraviolet light is electromagnetic radiation with a wavelength shorter than that of visible light, but longer than X-rays, in the range 10 nm to 400 nm, and energies from 3 eV to 124 eV...
, and infrared
Infrared
Infrared light is electromagnetic radiation with a wavelength longer than that of visible light, measured from the nominal edge of visible red light at 0.74 micrometres , and extending conventionally to 300 µm...
light. Because light is an electromagnetic wave, other forms of electromagnetic radiation
Electromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...
such as X-ray
X-ray
X-radiation is a form of electromagnetic radiation. X-rays have a wavelength in the range of 0.01 to 10 nanometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz and energies in the range 120 eV to 120 keV. They are shorter in wavelength than UV rays and longer than gamma...
s, microwave
Microwave
Microwaves, a subset of radio waves, have wavelengths ranging from as long as one meter to as short as one millimeter, or equivalently, with frequencies between 300 MHz and 300 GHz. This broad definition includes both UHF and EHF , and various sources use different boundaries...
s, and radio wave
Radio Wave
Radio Wave may refer to:*Radio frequency*Radio Wave 96.5, a radio station in Blackpool, UK...
s exhibit similar properties.
Most optical phenomena can be accounted for using the classical electromagnetic
Classical electromagnetism
Classical electromagnetism is a branch of theoretical physics that studies consequences of the electromagnetic forces between electric charges and currents...
description of light. Complete electromagnetic descriptions of light are, however, often difficult to apply in practice. Practical optics is usually done using simplified models. The most common of these, geometric optics, treats light as a collection of ray
Ray (optics)
In optics, a ray is an idealized narrow beam of light. Rays are used to model the propagation of light through an optical system, by dividing the real light field up into discrete rays that can be computationally propagated through the system by the techniques of ray tracing. This allows even very...
s that travel in straight lines and bend when they pass through or reflect from surfaces. Physical optics
Physical optics
In physics, physical optics, or wave optics, is the branch of optics which studies interference, diffraction, polarization, and other phenomena for which the ray approximation of geometric optics is not valid...
is a more comprehensive model of light, which includes wave
Wave
In physics, a wave is a disturbance that travels through space and time, accompanied by the transfer of energy.Waves travel and the wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium—that is, with little or no associated mass...
effects such as diffraction
Diffraction
Diffraction refers to various phenomena which occur when a wave encounters an obstacle. Italian scientist Francesco Maria Grimaldi coined the word "diffraction" and was the first to record accurate observations of the phenomenon in 1665...
and interference that cannot be accounted for in geometric optics. Historically, the ray-based model of light was developed first, followed by the wave model of light. Progress in electromagnetic theory in the 19th century led to the discovery that light waves were in fact electromagnetic radiation.
Some phenomena depend on the fact that light has both wave-like and particle-like properties. Explanation of these effects requires quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
. When considering light's particle-like properties, the light is modeled as a collection of particles called "photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
s". Quantum optics
Quantum optics
Quantum optics is a field of research in physics, dealing with the application of quantum mechanics to phenomena involving light and its interactions with matter.- History of quantum optics :...
deals with the application of quantum mechanics to optical systems.
Optical science is relevant to and studied in many related disciplines including astronomy
Astronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...
, various engineering
Engineering
Engineering is the discipline, art, skill and profession of acquiring and applying scientific, mathematical, economic, social, and practical knowledge, in order to design and build structures, machines, devices, systems, materials and processes that safely realize improvements to the lives of...
fields, photography
Photography
Photography is the art, science and practice of creating durable images by recording light or other electromagnetic radiation, either electronically by means of an image sensor or chemically by means of a light-sensitive material such as photographic film...
, and medicine
Medicine
Medicine is the science and art of healing. It encompasses a variety of health care practices evolved to maintain and restore health by the prevention and treatment of illness....
(particularly ophthalmology
Ophthalmology
Ophthalmology is the branch of medicine that deals with the anatomy, physiology and diseases of the eye. An ophthalmologist is a specialist in medical and surgical eye problems...
and optometry
Optometry
Optometry is a health care profession concerned with eyes and related structures, as well as vision, visual systems, and vision information processing in humans. Optometrists, or Doctors of Optometry, are state licensed medical professionals trained to prescribe and fit lenses to improve vision,...
). Practical applications of optics are found in a variety of technologies and everyday objects, including mirror
Mirror
A mirror is an object that reflects light or sound in a way that preserves much of its original quality prior to its contact with the mirror. Some mirrors also filter out some wavelengths, while preserving other wavelengths in the reflection...
s, lenses, telescopes
Optical telescope
An optical telescope is a telescope which is used to gather and focus light mainly from the visible part of the electromagnetic spectrum for directly viewing a magnified image for making a photograph, or collecting data through electronic image sensors....
, microscope
Microscope
A microscope is an instrument used to see objects that are too small for the naked eye. The science of investigating small objects using such an instrument is called microscopy...
s, lasers, and fiber optics.
History
Optics began with the development of lenses by the ancient EgyptAncient Egypt
Ancient Egypt was an ancient civilization of Northeastern Africa, concentrated along the lower reaches of the Nile River in what is now the modern country of Egypt. Egyptian civilization coalesced around 3150 BC with the political unification of Upper and Lower Egypt under the first pharaoh...
ians and Mesopotamia
Mesopotamia
Mesopotamia is a toponym for the area of the Tigris–Euphrates river system, largely corresponding to modern-day Iraq, northeastern Syria, southeastern Turkey and southwestern Iran.Widely considered to be the cradle of civilization, Bronze Age Mesopotamia included Sumer and the...
ns. The earliest known lenses were made from polished crystal, often quartz
Quartz
Quartz is the second-most-abundant mineral in the Earth's continental crust, after feldspar. It is made up of a continuous framework of SiO4 silicon–oxygen tetrahedra, with each oxygen being shared between two tetrahedra, giving an overall formula SiO2. There are many different varieties of quartz,...
, and have been dated as early as 700 BC for Assyria
Assyria
Assyria was a Semitic Akkadian kingdom, extant as a nation state from the mid–23rd century BC to 608 BC centred on the Upper Tigris river, in northern Mesopotamia , that came to rule regional empires a number of times through history. It was named for its original capital, the ancient city of Assur...
n lenses such as the Layard/Nimrud lens
Nimrud lens
The Nimrud lens is a 3000 year old piece of rock crystal, which was unearthed by Austen Henry Layard at the Assyrian palace of Nimrud, in modern-day Iraq. It may have been used as a magnifying glass, or as a burning-glass to start fires by concentrating sunlight. Assyrian craftsmen made intricate...
. The ancient Romans and Greeks
Ancient Greece
Ancient Greece is a civilization belonging to a period of Greek history that lasted from the Archaic period of the 8th to 6th centuries BC to the end of antiquity. Immediately following this period was the beginning of the Early Middle Ages and the Byzantine era. Included in Ancient Greece is the...
filled glass spheres with water to make lenses. These practical developments were followed by the development of theories of light and vision by ancient Greek
Greek philosophy
Ancient Greek philosophy arose in the 6th century BCE and continued through the Hellenistic period, at which point Ancient Greece was incorporated in the Roman Empire...
and Indian
Indian philosophy
India has a rich and diverse philosophical tradition dating back to ancient times. According to Radhakrishnan, the earlier Upanisads constitute "...the earliest philosophical compositions of the world."...
philosophers, and the development of geometrical optics
Geometrical optics
Geometrical optics, or ray optics, describes light propagation in terms of "rays". The "ray" in geometric optics is an abstraction, or "instrument", which can be used to approximately model how light will propagate. Light rays are defined to propagate in a rectilinear path as far as they travel in...
in the Greco-Roman world
Greco-Roman world
The Greco-Roman world, Greco-Roman culture, or the term Greco-Roman , when used as an adjective, as understood by modern scholars and writers, refers to those geographical regions and countries that culturally were directly, protractedly and intimately influenced by the language, culture,...
. The word optics comes from the ancient Greek
Ancient Greek
Ancient Greek is the stage of the Greek language in the periods spanning the times c. 9th–6th centuries BC, , c. 5th–4th centuries BC , and the c. 3rd century BC – 6th century AD of ancient Greece and the ancient world; being predated in the 2nd millennium BC by Mycenaean Greek...
word , meaning appearance or look. Plato
Plato
Plato , was a Classical Greek philosopher, mathematician, student of Socrates, writer of philosophical dialogues, and founder of the Academy in Athens, the first institution of higher learning in the Western world. Along with his mentor, Socrates, and his student, Aristotle, Plato helped to lay the...
first articulated emission theory
Emission theory (vision)
Emission theory or extramission theory is the proposal that visual perception is accomplished by rays of light emitted by the eyes. This theory has been replaced by intromission theory, which states that visual perception comes from something representative of the object entering the eyes...
, the idea that visual perception
Visual perception
Visual perception is the ability to interpret information and surroundings from the effects of visible light reaching the eye. The resulting perception is also known as eyesight, sight, or vision...
is accomplished by rays emitted by the eyes. He also commented on the parity
Parity (physics)
In physics, a parity transformation is the flip in the sign of one spatial coordinate. In three dimensions, it is also commonly described by the simultaneous flip in the sign of all three spatial coordinates:...
reversal of mirrors in Timaeus
Timaeus (dialogue)
Timaeus is one of Plato's dialogues, mostly in the form of a long monologue given by the title character, written circa 360 BC. The work puts forward speculation on the nature of the physical world and human beings. It is followed by the dialogue Critias.Speakers of the dialogue are Socrates,...
. Some hundred years later, Euclid
Euclid
Euclid , fl. 300 BC, also known as Euclid of Alexandria, was a Greek mathematician, often referred to as the "Father of Geometry". He was active in Alexandria during the reign of Ptolemy I...
wrote a treatise entitled Optics wherein he described the mathematical rules of perspective
Perspective (graphical)
Perspective in the graphic arts, such as drawing, is an approximate representation, on a flat surface , of an image as it is seen by the eye...
and describes the effects of refraction qualitatively. Ptolemy
Ptolemy
Claudius Ptolemy , was a Roman citizen of Egypt who wrote in Greek. He was a mathematician, astronomer, geographer, astrologer, and poet of a single epigram in the Greek Anthology. He lived in Egypt under Roman rule, and is believed to have been born in the town of Ptolemais Hermiou in the...
, in his treatise Optics, summarizes much of Euclid and goes on to describe a way to measure the angle of refraction, though he failed to notice the empirical relationship between it and the angle of incidence.
Middle Ages
The Middle Ages is a periodization of European history from the 5th century to the 15th century. The Middle Ages follows the fall of the Western Roman Empire in 476 and precedes the Early Modern Era. It is the middle period of a three-period division of Western history: Classic, Medieval and Modern...
, Greek ideas about optics were resurrected and extended by writers in the Muslim world
Muslim world
The term Muslim world has several meanings. In a religious sense, it refers to those who adhere to the teachings of Islam, referred to as Muslims. In a cultural sense, it refers to Islamic civilization, inclusive of non-Muslims living in that civilization...
. One of the earliest of these was Al-Kindi
Al-Kindi
' , known as "the Philosopher of the Arabs", was a Muslim Arab philosopher, mathematician, physician, and musician. Al-Kindi was the first of the Muslim peripatetic philosophers, and is unanimously hailed as the "father of Islamic or Arabic philosophy" for his synthesis, adaptation and promotion...
(c. 801–73). In 984, the Persian mathematician Ibn Sahl
Ibn Sahl
This article is about the physicist. For the physician, see Ali ibn Sahl Rabban al-Tabari. For the poet, see Ibn Sahl of Sevilla.Ibn Sahl was a Muslim Persian mathematician, physicist and optics engineer of the Islamic Golden Age associated with the Abbasid court of Baghdad...
wrote the treatise "On burning mirrors and lenses", correctly describing a law of refraction equivalent to Snell's law. He used this law to compute optimum shapes for lenses and curved mirror
Curved mirror
A curved mirror is a mirror with a curved reflective surface, which may be either convex or concave . Most curved mirrors have surfaces that are shaped like part of a sphere, but other shapes are sometimes used in optical devices...
s. In the early 11th century, Alhazen (Ibn al-Haytham) wrote his Book of Optics
Book of Optics
The Book of Optics ; ; Latin: De Aspectibus or Opticae Thesaurus: Alhazeni Arabis; Italian: Deli Aspecti) is a seven-volume treatise on optics and other fields of study composed by the medieval Muslim scholar Alhazen .-See also:* Science in medieval Islam...
, which documented the then-current understanding of vision.
In the 13th century, Roger Bacon
Roger Bacon
Roger Bacon, O.F.M. , also known as Doctor Mirabilis , was an English philosopher and Franciscan friar who placed considerable emphasis on the study of nature through empirical methods...
used parts of glass spheres as magnifying glass
Magnifying glass
A magnifying glass is a convex lens that is used to produce a magnified image of an object. The lens is usually mounted in a frame with a handle ....
es, and discovered that light reflects from objects rather than being released from them. In Italy, around 1284, Salvino D'Armate
Salvino D'Armate
Salvino D'Armato degli Armati of Florence is one of the possible inventors of eyeglasses. It was previously thought that he invented eyeglasses around 1284, although the evidence now suggests that this was a hoax....
invented the first wearable eyeglasses.
The earliest known telescopes were refracting telescope
Refracting telescope
A refracting or refractor telescope is a type of optical telescope that uses a lens as its objective to form an image . The refracting telescope design was originally used in spy glasses and astronomical telescopes but is also used for long focus camera lenses...
s developed within the Netherlands
Netherlands
The Netherlands is a constituent country of the Kingdom of the Netherlands, located mainly in North-West Europe and with several islands in the Caribbean. Mainland Netherlands borders the North Sea to the north and west, Belgium to the south, and Germany to the east, and shares maritime borders...
eyeglass industry in 1608 with contemporaneous or after the fact claims of invention citing three individuals: Hans Lippershey
Hans Lippershey
Hans Lippershey , also known as Johann Lippershey or Lipperhey, was a German-Dutch lensmaker commonly associated with the invention of the telescope, although it is unclear if he was the first to build one.-Biography:...
and Zacharias Janssen
Zacharias Janssen
Zacharias Jansen was a Dutch spectacle-maker from Middelburg associated with the invention of the first optical telescope. Jansen is sometimes also credited for inventing the first truly compound microscope...
, who were spectacle makers in Middelburg
Middelburg
Middelburg is a municipality and a city in the south-western Netherlands and the capital of the province of Zeeland. It is situated in the Midden-Zeeland region. It has a population of about 48,000.- History of Middelburg :...
, and Jacob Metius
Jacob Metius
Jacob Metius was a Dutch instrument-maker and a specialist in grinding lenses. He was born in Alkmaar and was the brother of Adriaan Adriaanszoon...
of Alkmaar
Alkmaar
Alkmaar is a municipality and a city in the Netherlands, in the province of Noord Holland. Alkmaar is well known for its traditional cheese market. For tourists, it is a popular cultural destination.-History:...
. In Italy, Galileo
Galileo Galilei
Galileo Galilei , was an Italian physicist, mathematician, astronomer, and philosopher who played a major role in the Scientific Revolution. His achievements include improvements to the telescope and consequent astronomical observations and support for Copernicanism...
greatly improved upon these designs the following year. In 1668, Isaac Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...
constructed the first practical reflecting telescope
Reflecting telescope
A reflecting telescope is an optical telescope which uses a single or combination of curved mirrors that reflect light and form an image. The reflecting telescope was invented in the 17th century as an alternative to the refracting telescope which, at that time, was a design that suffered from...
, which bears his name, the Newtonian reflector
Newtonian telescope
The Newtonian telescope is a type of reflecting telescope invented by the British scientist Sir Isaac Newton , using a concave primary mirror and a flat diagonal secondary mirror. Newton’s first reflecting telescope was completed in 1668 and is the earliest known functional reflecting telescope...
.
The first microscope was made around 1595, also in Middelburg. Three different eyeglass makers have been given credit for the invention: Lippershey, Janssen, and his father, Hans. The coining of the name "microscope" has been credited to Giovanni Faber
Giovanni Faber
Giovanni Faber was a German papal doctor, botanist and art collector, originally from Bamberg in Bavaria, who lived in Rome from 1598. He was curator of the Vatican botanical garden, a member and the secretary of the Accademia dei Lincei. He acted throughout his career as a political broker...
, who gave that name to Galileo's compound microscope in 1625.
Optical theory progressed in the mid-17th century with treatises written by philosopher René Descartes
René Descartes
René Descartes ; was a French philosopher and writer who spent most of his adult life in the Dutch Republic. He has been dubbed the 'Father of Modern Philosophy', and much subsequent Western philosophy is a response to his writings, which are studied closely to this day...
, which explained a variety of optical phenomena including reflection and refraction by assuming that light was emitted by objects which produced it. This differed substantively from the ancient Greek emission theory. In the late 1660s and early 1670s, Newton expanded Descartes' ideas into a corpuscle theory of light, famously showing that white light, instead of being a unique color, was really a composite of different colors that can be separated into a spectrum
Spectrum
A spectrum is a condition that is not limited to a specific set of values but can vary infinitely within a continuum. The word saw its first scientific use within the field of optics to describe the rainbow of colors in visible light when separated using a prism; it has since been applied by...
with a prism
Prism (optics)
In optics, a prism is a transparent optical element with flat, polished surfaces that refract light. The exact angles between the surfaces depend on the application. The traditional geometrical shape is that of a triangular prism with a triangular base and rectangular sides, and in colloquial use...
. In 1690, Christian Huygens proposed a wave theory for light based on suggestions that had been made by Robert Hooke
Robert Hooke
Robert Hooke FRS was an English natural philosopher, architect and polymath.His adult life comprised three distinct periods: as a scientific inquirer lacking money; achieving great wealth and standing through his reputation for hard work and scrupulous honesty following the great fire of 1666, but...
in 1664. Hooke himself publicly criticized Newton's theories of light and the feud between the two lasted until Hooke's death. In 1704, Newton published Opticks
Opticks
Opticks is a book written by English physicist Isaac Newton that was released to the public in 1704. It is about optics and the refraction of light, and is considered one of the great works of science in history...
and, at the time, partly because of his success in other areas of physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
, he was generally considered to be the victor in the debate over the nature of light.
Newtonian optics was generally accepted until the early 19th century when Thomas Young
Thomas Young (scientist)
Thomas Young was an English polymath. He is famous for having partly deciphered Egyptian hieroglyphics before Jean-François Champollion eventually expanded on his work...
and Augustin-Jean Fresnel
Augustin-Jean Fresnel
Augustin-Jean Fresnel , was a French engineer who contributed significantly to the establishment of the theory of wave optics. Fresnel studied the behaviour of light both theoretically and experimentally....
conducted experiments on the interference of light that firmly established light's wave nature. Young's famous double slit experiment
Young's interference experiment
Young's interference experiment, also called Young's double-slit interferometer, was the original version of the modern double-slit experiment, performed at the beginning of the nineteenth century by Thomas Young. This experiment played a major role in the general acceptance of the wave theory of...
showed that light followed the law of superposition
Law of superposition
The law of superposition is a key axiom based on observations of natural history that is a foundational principle of sedimentary stratigraphy and so of other geology dependent natural sciences:...
, which is a wave-like property not predicted by Newton's corpuscle theory. This work led to a theory of diffraction for light and opened an entire area of study in physical optics. Wave optics was successfully unified with electromagnetic theory by James Clerk Maxwell
James Clerk Maxwell
James Clerk Maxwell of Glenlair was a Scottish physicist and mathematician. His most prominent achievement was formulating classical electromagnetic theory. This united all previously unrelated observations, experiments and equations of electricity, magnetism and optics into a consistent theory...
in the 1860s.
The next development in optical theory came in 1899 when Max Planck
Max Planck
Max Karl Ernst Ludwig Planck, ForMemRS, was a German physicist who actualized the quantum physics, initiating a revolution in natural science and philosophy. He is regarded as the founder of the quantum theory, for which he received the Nobel Prize in Physics in 1918.-Life and career:Planck came...
correctly modeled blackbody radiation by assuming that the exchange of energy between light and matter only occurred in discrete amounts he called quanta. In 1905, Albert Einstein
Albert Einstein
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...
published the theory of the photoelectric effect
Photoelectric effect
In the photoelectric effect, electrons are emitted from matter as a consequence of their absorption of energy from electromagnetic radiation of very short wavelength, such as visible or ultraviolet light. Electrons emitted in this manner may be referred to as photoelectrons...
that firmly established the quantization of light itself. In 1913, Niels Bohr
Niels Bohr
Niels Henrik David Bohr was a Danish physicist who made foundational contributions to understanding atomic structure and quantum mechanics, for which he received the Nobel Prize in Physics in 1922. Bohr mentored and collaborated with many of the top physicists of the century at his institute in...
showed that atoms could only emit discrete amounts of energy, thus explaining the discrete lines seen in emission
Emission spectrum
The emission spectrum of a chemical element or chemical compound is the spectrum of frequencies of electromagnetic radiation emitted by the element's atoms or the compound's molecules when they are returned to a lower energy state....
and absorption spectra. The understanding of the interaction between light and matter, which followed from these developments, not only formed the basis of quantum optics but also was crucial for the development
History of quantum mechanics
The history of quantum mechanics, as it interlaces with the history of quantum chemistry, began essentially with a number of different scientific discoveries: the 1838 discovery of cathode rays by Michael Faraday; the 1859-1860 winter statement of the black body radiation problem by Gustav...
of quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
as a whole. The ultimate culmination was the theory of quantum electrodynamics
Quantum electrodynamics
Quantum electrodynamics is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved...
, which explains all optics and electromagnetic processes in general as being the result of the exchange of real and virtual photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
s.
Quantum optics gained practical importance with the invention of the maser
Maser
A maser is a device that produces coherent electromagnetic waves through amplification by stimulated emission. Historically, “maser” derives from the original, upper-case acronym MASER, which stands for "Microwave Amplification by Stimulated Emission of Radiation"...
in 1953 and the laser in 1960. Following the work of Paul Dirac
Paul Dirac
Paul Adrien Maurice Dirac, OM, FRS was an English theoretical physicist who made fundamental contributions to the early development of both quantum mechanics and quantum electrodynamics...
in quantum field theory
Quantum field theory
Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...
, George Sudarshan
George Sudarshan
Ennackal Chandy George Sudarshan , also E.C.G. Sudarshan, is a prominent Indian American physicist, author, and professor at The University of Texas at Austin.-Early life:...
, Roy J. Glauber
Roy J. Glauber
Roy Jay Glauber is an American theoretical physicist. He is the Mallinckrodt Professor of Physics at Harvard University and Adjunct Professor of Optical Sciences at the University of Arizona...
, and Leonard Mandel
Leonard Mandel
Leonard Mandel was the Lee DuBridge Professor Emeritus of Physics and Optics at the University of Rochester when he died at the age of 73 at his home in Pittsford, New York. He contributed immensely to theoretical and experimental optics...
applied quantum theory to the electromagnetic field in the 1950s and 1960s to gain a more detailed understanding of photodetection and the statistics
Statistical mechanics
Statistical mechanics or statistical thermodynamicsThe terms statistical mechanics and statistical thermodynamics are used interchangeably...
of light.
Classical optics
Classical optics is divided into two main branches: geometrical optics and physical optics. In geometrical, or ray optics, light is considered to travel in straight lines, and in physical, or wave optics, light is considered to be an electromagnetic wave.Geometrical optics can be viewed as an approximation of physical optics which can be applied when the wavelength of the light used is much smaller than the size of the optical elements or system being modelled.
Geometrical optics
Geometrical optics, or ray optics, describes the propagationWave propagation
Wave propagation is any of the ways in which waves travel.With respect to the direction of the oscillation relative to the propagation direction, we can distinguish between longitudinal wave and transverse waves....
of light in terms of "rays" which travel in straight lines, and whose paths are governed by the laws of reflection and refraction at interfaces between different media. These laws were discovered empirically as far back as 984AD and have been used in the design of optical components and instruments from then until the present day. They can be summarised as follows:
When a ray of light hits the boundary between two transparent materials, it is divided into a reflected and a refracted ray.
- The law of reflection says that the reflected ray lies in the plane of incidence, and the angle of reflection equals the angle of incidence.
- The law of refraction says that the refracted ray lies in the plane of incidence, and the sine of the angle of refraction divided by the sine of the angle of incidence is a constant.
where is a constant for any two materials and a given colour of light. It is known as the refractive index
Refractive index
In optics the refractive index or index of refraction of a substance or medium is a measure of the speed of light in that medium. It is expressed as a ratio of the speed of light in vacuum relative to that in the considered medium....
.
The laws of reflection and refraction can be derived from Fermat's principle
Fermat's principle
In optics, Fermat's principle or the principle of least time is the principle that the path taken between two points by a ray of light is the path that can be traversed in the least time. This principle is sometimes taken as the definition of a ray of light...
which states that the path taken between two points by a ray of light is the path that can be traversed in the least time.
Approximations
Geometrical optics is often simplified by making the paraxial approximationParaxial approximation
In geometric optics, the paraxial approximation is a small-angle approximation used in Gaussian optics and ray tracing of light through an optical system ....
, or "small angle approximation." The mathematical behavior then becomes linear, allowing optical components and systems to be described by simple matrices. This leads to the techniques of Gaussian optics
Gaussian optics
Gaussian optics is a technique in geometrical optics that describes the behaviour of light rays in optical systems by using the paraxial approximation, in which only rays which make small angles with the optical axis of the system are considered. In this approximation, trigonometric functions can...
and paraxial ray tracing
Ray tracing (physics)
In physics, ray tracing is a method for calculating the path of waves or particles through a system with regions of varying propagation velocity, absorption characteristics, and reflecting surfaces. Under these circumstances, wavefronts may bend, change direction, or reflect off surfaces,...
, which are used to find basic properties of optical systems, such as approximate image
Image
An image is an artifact, for example a two-dimensional picture, that has a similar appearance to some subject—usually a physical object or a person.-Characteristics:...
and object positions and magnification
Magnification
Magnification is the process of enlarging something only in appearance, not in physical size. This enlargement is quantified by a calculated number also called "magnification"...
s.
Reflections
Specular reflection
Specular reflection is the mirror-like reflection of light from a surface, in which light from a single incoming direction is reflected into a single outgoing direction...
and diffuse reflection
Diffuse reflection
Diffuse reflection is the reflection of light from a surface such that an incident ray is reflected at many angles rather than at just one angle as in the case of specular reflection...
. Specular reflection describes the gloss of surfaces such as mirrors, which reflect light in a simple, predictable way. This allows for production of reflected images that can be associated with an actual (real
Real image
In optics, a real image is a representation of an object in which the perceived location is actually a point of convergence of the rays of light that make up the image. If a screen is placed in the plane of a real image the image will generally become visible on the screen...
) or extrapolated (virtual
Virtual image
In optics, a virtual image is an image in which the outgoing rays from a point on the object always diverge. It will appear to converge in or behind the optical device . A simple example is a flat mirror where the image of oneself is perceived at twice the distance from oneself to the mirror...
) location in space. Diffuse reflection describes opaque, non limpid materials, such as paper or rock. The reflections from these surfaces can only be described statistically, with the exact distribution of the reflected light depending on the microscopic structure of the material. Many diffuse reflectors are described or can be approximated by Lambert's cosine law
Lambert's cosine law
In optics, Lambert's cosine law says that the radiant intensity observed from a Lambertian surface or a Lambertian radiator is directly proportional to the cosine of the angle θ between the observer's line of sight and the surface normal. A Lambertian surface is also known as an ideal diffusely...
, which describes surfaces that have equal luminance
Luminance
Luminance is a photometric measure of the luminous intensity per unit area of light travelling in a given direction. It describes the amount of light that passes through or is emitted from a particular area, and falls within a given solid angle. The SI unit for luminance is candela per square...
when viewed from any angle. Glossy surfaces can give both specular and diffuse reflection.
In specular reflection, the direction of the reflected ray is determined by the angle the incident ray makes with the surface normal
Surface normal
A surface normal, or simply normal, to a flat surface is a vector that is perpendicular to that surface. A normal to a non-flat surface at a point P on the surface is a vector perpendicular to the tangent plane to that surface at P. The word "normal" is also used as an adjective: a line normal to a...
, a line perpendicular to the surface at the point where the ray hits. The incident and reflected rays and the normal lie in a single plane, and the angle between the reflected ray and the surface normal is the same as that between the incident ray and the normal. This is known as the Law of Reflection.
For flat mirrors
Plane mirror
A plane mirror is a mirror with a plane reflective surface.For light rays striking a plane mirror, the angle of reflection equals the angle of incidence...
, the law of reflection implies that images of objects are upright and the same distance behind the mirror as the objects are in front of the mirror. The image size is the same as the object size. The law also implies that mirror image
Mirror image
A mirror image is a reflected duplication of an object that appears identical but reversed. As an optical effect it results from reflection off of substances such as a mirror or water. It is also a concept in geometry and can be used as a conceptualization process for 3-D structures...
s are parity inverted
Parity (physics)
In physics, a parity transformation is the flip in the sign of one spatial coordinate. In three dimensions, it is also commonly described by the simultaneous flip in the sign of all three spatial coordinates:...
, which we perceive as a left-right inversion. Images formed from reflection in two (or any even number of) mirrors are not parity inverted. Corner reflector
Corner reflector
A corner reflector is a retroreflector consisting of three mutually perpendicular, intersecting flat surfaces, which reflects waves back directly towards the source, but shifted . Unlike a simple mirror, they work for a relatively wide-angle field of view. The three intersecting surfaces often have...
s retroreflect
Retroreflector
A retroreflector is a device or surface that reflects light back to its source with a minimum scattering of light. An electromagnetic wave front is reflected back along a vector that is parallel to but opposite in direction from the wave's source. The device or surface's angle of incidence is...
light, producing reflected rays that travel back in the direction from which the incident rays came.
Mirrors with curved surfaces
Curved mirror
A curved mirror is a mirror with a curved reflective surface, which may be either convex or concave . Most curved mirrors have surfaces that are shaped like part of a sphere, but other shapes are sometimes used in optical devices...
can be modeled by ray-tracing
Ray tracing (physics)
In physics, ray tracing is a method for calculating the path of waves or particles through a system with regions of varying propagation velocity, absorption characteristics, and reflecting surfaces. Under these circumstances, wavefronts may bend, change direction, or reflect off surfaces,...
and using the law of reflection at each point on the surface. For mirrors with parabolic surfaces
Parabolic reflector
A parabolic reflector is a reflective device used to collect or project energy such as light, sound, or radio waves. Its shape is that of a circular paraboloid, that is, the surface generated by a parabola revolving around its axis...
, parallel rays incident on the mirror produce reflected rays that converge at a common focus
Focus (optics)
In geometrical optics, a focus, also called an image point, is the point where light rays originating from a point on the object converge. Although the focus is conceptually a point, physically the focus has a spatial extent, called the blur circle. This non-ideal focusing may be caused by...
. Other curved surfaces may also focus light, but with aberrations due to the diverging shape causing the focus to be smeared out in space. In particular, spherical mirrors exhibit spherical aberration
Spherical aberration
thumb|right|Spherical aberration. A perfect lens focuses all incoming rays to a point on the [[Optical axis|optic axis]]. A real lens with spherical surfaces suffers from spherical aberration: it focuses rays more tightly if they enter it far from the optic axis than if they enter closer to the...
. Curved mirrors can form images with magnification greater than or less than one, and the magnification can be negative, indicating that the image is inverted. An upright image formed by reflection in a mirror is always virtual, while an inverted image is real and can be projected onto a screen.
Refractions
and another medium with index of refraction . In such situations, Snell's LawSnell's law
In optics and physics, Snell's law is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water and glass...
describes the resulting deflection of the light ray:
where
and are the angles between the normal (to the interface) and the incident and refracted waves, respectively. This phenomenon is also associated with a changing speed of light as seen from the definition of index of refraction provided above which implies:where
and are the wave velocities through the respective media.Various consequences of Snell's Law include the fact that for light rays traveling from a material with a high index of refraction to a material with a low index of refraction, it is possible for the interaction with the interface to result in zero transmission. This phenomenon is called total internal reflection
Total internal reflection
Total internal reflection is an optical phenomenon that happens when a ray of light strikes a medium boundary at an angle larger than a particular critical angle with respect to the normal to the surface. If the refractive index is lower on the other side of the boundary and the incident angle is...
and allows for fiber optics technology. As light signals travel down a fiber optic cable, it undergoes total internal reflection allowing for essentially no light lost over the length of the cable. It is also possible to produce polarized light rays using a combination of reflection and refraction: When a refracted ray and the reflected ray form a right angle
Right angle
In geometry and trigonometry, a right angle is an angle that bisects the angle formed by two halves of a straight line. More precisely, if a ray is placed so that its endpoint is on a line and the adjacent angles are equal, then they are right angles...
, the reflected ray has the property of "plane polarization". The angle of incidence required for such a scenario is known as Brewster's angle.
Snell's Law can be used to predict the deflection of light rays as they pass through "linear media" as long as the indexes of refraction and the geometry of the media are known. For example, the propagation of light through a prism results in the light ray being deflected depending on the shape and orientation of the prism. Additionally, since different frequencies of light have slightly different indexes of refraction in most materials, refraction can be used to produce dispersion spectra that appear as rainbows. The discovery of this phenomenon when passing light through a prism is famously attributed to Isaac Newton.
Some media have an index of refraction which varies gradually with position and, thus, light rays curve through the medium rather than travel in straight lines. This effect is what is responsible for mirage
Mirage
A mirage is a naturally occurring optical phenomenon in which light rays are bent to produce a displaced image of distant objects or the sky. The word comes to English via the French mirage, from the Latin mirare, meaning "to look at, to wonder at"...
s seen on hot days where the changing index of refraction of the air causes the light rays to bend creating the appearance of specular reflections in the distance (as if on the surface of a pool of water). Material that has a varying index of refraction is called a gradient-index (GRIN) material and has many useful properties used in modern optical scanning technologies including photocopiers and scanners
Scanners
Scanners is a 1981 science-fiction horror film written and directed by David Cronenberg and starring Jennifer O'Neill, Stephen Lack, Michael Ironside, and Patrick McGoohan...
. The phenomenon is studied in the field of gradient-index optics.
) and object distance ():where
is the distance associated with the image and is considered by convention to be negative if on the same side of the lens as the object and positive if on the opposite side of the lens. The focal length f is considered negative for concave lenses.Likewise, the magnification of a lens is given by
where the negative sign is given, by convention, to indicate an upright object for positive values and an inverted object for negative values. Similar to mirrors, upright images produced by single lenses are virtual while inverted images are real.
Lenses suffer from aberrations that distort images and focal points. These are due to both to geometrical imperfections and due to the changing index of refraction for different wavelengths of light (chromatic aberration
Chromatic aberration
In optics, chromatic aberration is a type of distortion in which there is a failure of a lens to focus all colors to the same convergence point. It occurs because lenses have a different refractive index for different wavelengths of light...
).
Physical optics
In physical optics, light is considered to propagate as a waveWave
In physics, a wave is a disturbance that travels through space and time, accompanied by the transfer of energy.Waves travel and the wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium—that is, with little or no associated mass...
. This model predicts phenomena such as interference and diffraction
Diffraction
Diffraction refers to various phenomena which occur when a wave encounters an obstacle. Italian scientist Francesco Maria Grimaldi coined the word "diffraction" and was the first to record accurate observations of the phenomenon in 1665...
which are not explained by geometric optics. The speed of light
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...
waves is approximately 3.10 8 m/s. The wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
of visible light waves varies between 400-700nm but light waves are usually considered to also include infrared
Infrared
Infrared light is electromagnetic radiation with a wavelength longer than that of visible light, measured from the nominal edge of visible red light at 0.74 micrometres , and extending conventionally to 300 µm...
waves (0.7-300μm) and ultraviolet waves (10-400nm).
The wave model can be used to make predictions about how an optical system will behave without requiring an explanation of what is "waving" in what medium. Until the middle of the 19th century, most physicists believed in an "ethereal" medium in which the light disturbance propagated. The existence of electromagnetic waves was predicted in 1865 by Maxwell's equations. These waves propagate at the speed of light
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...
and have varying electric and magnetic fields which are orthogonal to one another, and also to the direction of propagation of the waves. Light waves are now generally treated as electromagnetic waves except when quantum mechanical effects have to be considered.
Modelling and design of optical systems using physical optics
Many simplifed approximations are available for analysing and designing optical systems. Most of these use a single scalarScalar (physics)
In physics, a scalar is a simple physical quantity that is not changed by coordinate system rotations or translations , or by Lorentz transformations or space-time translations . This is in contrast to a vector...
quantity to represent the electric field of the light wave, rather than using a vector
Vector
Vector, a Latin word meaning "carrier", may refer in English to:-In computer science:*A one-dimensional array**Vector , a data type in the C++ Standard Template Library...
model with orthogonal electric and magnetic vectors.
The Huygens–Fresnel equation is one such model. This was derived empirically by Fresnel in 1815, based on Huygen's hypothesis that each point on a wavefront generates a secondary spherical wavefront, which Fresnel combined with the principle of superposition
Superposition principle
In physics and systems theory, the superposition principle , also known as superposition property, states that, for all linear systems, the net response at a given place and time caused by two or more stimuli is the sum of the responses which would have been caused by each stimulus individually...
of waves. The Kirchoff diffraction equation
Kirchhoff's diffraction formula
Kirchhoff's diffraction formula can be used to model the propagation of light in a wide range of configurations, either analytically or using numerical modelling. It gives an expression for the wave disturbance when a monochromatic spherical wave passes through an opening in an opaque screen...
, which is derived using Maxwell's equations, puts the Huygens-Fresnel equation on a firmer physical foundation. Examples of the application of Huygens–Fresnel principle can be found in the sections on diffraction
Diffraction
Diffraction refers to various phenomena which occur when a wave encounters an obstacle. Italian scientist Francesco Maria Grimaldi coined the word "diffraction" and was the first to record accurate observations of the phenomenon in 1665...
and Fraunhofer diffraction
Fraunhofer diffraction (mathematics)
In optics, the Fraunhofer diffraction equation is used to model the diffraction of waves when the diffraction pattern is viewed at a long distance from the diffracting object, and also when it is viewed at the focal plane of an imaging lens....
.
More rigorous models, involving the modelling of both electric and magnetic fields of the light wave, are required when dealing with the detailed interaction of light with materials where the interaction depends on their electric and magnetic properties. For instance, the behaviour of a light wave interacting with a metal surface is quite different from what happens when it interacts with a di-electric material. A vector model must also be used to model polarized light.
Numerical modeling
Computer simulation
A computer simulation, a computer model, or a computational model is a computer program, or network of computers, that attempts to simulate an abstract model of a particular system...
techniques such as the Finite element method
Finite element method
The finite element method is a numerical technique for finding approximate solutions of partial differential equations as well as integral equations...
, the Boundary element method
Boundary element method
The boundary element method is a numerical computational method of solving linear partial differential equations which have been formulated as integral equations . It can be applied in many areas of engineering and science including fluid mechanics, acoustics, electromagnetics, and fracture...
and the Transmission-line matrix method can be used to model the propagation of light in systems which cannot be solved analytically. Such models are computationally demanding and are normally only used to solve small-scale problems that require accuracy beyond that which can be achieved with analytical solutions.
All of the results from geometrical optics can be recovered using the techniques of Fourier optics
Fourier optics
Fourier optics is the study of classical optics using Fourier transforms and can be seen as the dual of the Huygens-Fresnel principle. In the latter case, the wave is regarded as a superposition of expanding spherical waves which radiate outward from actual current sources via a Green's function...
which apply many of the same mathematical and analytical techniques used in acoustic engineering and signal processing
Signal processing
Signal processing is an area of systems engineering, electrical engineering and applied mathematics that deals with operations on or analysis of signals, in either discrete or continuous time...
.
Gaussian beam propagation
Gaussian beam
In optics, a Gaussian beam is a beam of electromagnetic radiation whose transverse electric field and intensity distributions are well approximated by Gaussian functions. Many lasers emit beams that approximate a Gaussian profile, in which case the laser is said to be operating on the fundamental...
is a simple paraxial physical optics model for the propagation of coherent radiation such as laser beams. This technique partially accounts for diffraction, allowing accurate calculations of the rate at which a laser beam expands with distance, and the minimum size to which the beam can be focused. Gaussian beam propagation thus bridges the gap between geometric and physical optics.
Superposition and interference
In the absence of nonlinearNonlinear optics
Nonlinear optics is the branch of optics that describes the behavior of light in nonlinear media, that is, media in which the dielectric polarization P responds nonlinearly to the electric field E of the light...
effects, the superposition principle
Superposition principle
In physics and systems theory, the superposition principle , also known as superposition property, states that, for all linear systems, the net response at a given place and time caused by two or more stimuli is the sum of the responses which would have been caused by each stimulus individually...
can be used to predict the shape of interacting waveforms through the simple addition of the disturbances. This interaction of waves to produce a resulting pattern is generally termed "interference" and can result in a variety of outcomes. If two waves of the same wavelength and frequency are in phase
Phase (waves)
Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...
, both the wave crests and wave troughs align. This results in constructive interference and an increase in the amplitude of the wave, which for light is associated with a brightening of the waveform in that location. Alternatively, if the two waves of the same wavelength and frequency are out of phase, then the wave crests will align with wave troughs and vice-versa. This results in destructive interference and a decrease in the amplitude of the wave, which for light is associated with a dimming of the waveform at that location. See below for an illustration of this effect.
| combined waveform |
||
| wave 1 | ||
| wave 2 | ||
| Two waves in phase | Two waves 180° out of phase |
|
Interferometry
Interferometry refers to a family of techniques in which electromagnetic waves are superimposed in order to extract information about the waves. An instrument used to interfere waves is called an interferometer. Interferometry is an important investigative technique in the fields of astronomy,...
is the science of measuring these patterns, usually as a means of making precise determinations of distances or angular resolution
Angular resolution
Angular resolution, or spatial resolution, describes the ability of any image-forming device such as an optical or radio telescope, a microscope, a camera, or an eye, to distinguish small details of an object...
s. The Michelson interferometer
Michelson interferometer
The Michelson interferometer is the most common configuration for optical interferometry and was invented by Albert Abraham Michelson. An interference pattern is produced by splitting a beam of light into two paths, bouncing the beams back and recombining them...
was a famous instrument which used interference effects to accurately measure the speed of light.
The appearance of thin films and coatings is directly affected by interference effects. Antireflective coatings use destructive interference to reduce the reflectivity of the surfaces they coat, and can be used to minimize glare and unwanted reflections. The simplest case is a single layer with thickness one-fourth the wavelength of incident light. The reflected wave from the top of the film and the reflected wave from the film/material interface are then exactly 180° out of phase, causing destructive interference. The waves are only exactly out of phase for one wavelength, which would typically be chosen to be near the center of the visible spectrum, around 550 nm. More complex designs using multiple layers can achieve low reflectivity over a broad band, or extremely low reflectivity at a single wavelength.
Constructive interference in thin films can create strong reflection of light in a range of wavelengths, which can be narrow or broad depending on the design of the coating. These films are used to make dielectric mirror
Dielectric mirror
A dielectric mirror is a type of a mirror composed of multiple thin layers of dielectric material, typically deposited on a substrate of glass or some other optical material. By careful choice of the type and thickness of the dielectric layers, one can design an optical coating with specified...
s, interference filter
Interference filter
An interference filter or dichroic filter is an optical filter that reflects one or more spectral bands or lines and transmits others, while maintaining a nearly zero coefficient of absorption for all wavelengths of interest...
s, heat reflectors, and filters for color separation in color television
Color television
Color television is part of the history of television, the technology of television and practices associated with television's transmission of moving images in color video....
cameras. This interference effect is also what causes the colorful rainbow patterns seen in oil slicks.
Diffraction and optical resolution
Diffraction is the process by which light interference is most commonly observed. The effect was first described in 1665 by Francesco Maria GrimaldiFrancesco Maria Grimaldi
Francesco Maria Grimaldi was an Italian Jesuit priest, mathematician and physicist who taught at the Jesuit college in Bologna....
, who also coined the term from the Latin diffringere, 'to break into pieces'. Later that century, Robert Hooke and Isaac Newton also described phenomena now known to be diffraction in Newton's rings
Newton's rings
The phenomenon of Newton's rings, named after Isaac Newton who first studied them in 1717, is an interference pattern caused by the reflection of light between two surfaces - a spherical surface and an adjacent flat surface...
while James Gregory
James Gregory (astronomer and mathematician)
James Gregory FRS was a Scottish mathematician and astronomer. He described an early practical design for the reflecting telescope – the Gregorian telescope – and made advances in trigonometry, discovering infinite series representations for several trigonometric functions.- Biography :The...
recorded his observations of diffraction patterns from bird feathers.
The first physical optics model of diffraction that relied on the Huygens–Fresnel principle was developed in 1803 by Thomas Young
Thomas Young (scientist)
Thomas Young was an English polymath. He is famous for having partly deciphered Egyptian hieroglyphics before Jean-François Champollion eventually expanded on his work...
in his interference experiments
Young's interference experiment
Young's interference experiment, also called Young's double-slit interferometer, was the original version of the modern double-slit experiment, performed at the beginning of the nineteenth century by Thomas Young. This experiment played a major role in the general acceptance of the wave theory of...
with the interference patterns of two closely spaced slits. Young showed that his results could only be explained if the two slits acted as two unique sources of waves rather than corpuscles. In 1815 and 1818, Augustin-Jean Fresnel firmly established the mathematics of how wave interference can account for diffraction.
The simplest physical models of diffraction use equations that describe the angular separation of light and dark fringes due to light of a particular wavelength (
). In general, the equation takes the formwhere
is the separation between two wavefront sources (in the case of Young's experiments, it was two slitsDouble-slit experiment
The double-slit experiment, sometimes called Young's experiment, is a demonstration that matter and energy can display characteristics of both waves and particles...
),
is the angular separation between the central fringe and the th order fringe, where the central maximum is .This equation is modified slightly to take into account a variety of situations such as diffraction through a single gap, diffraction through multiple slits, or diffraction through a diffraction grating
Diffraction grating
In optics, a diffraction grating is an optical component with a periodic structure, which splits and diffracts light into several beams travelling in different directions. The directions of these beams depend on the spacing of the grating and the wavelength of the light so that the grating acts as...
that contains a large number of slits at equal spacing. More complicated models of diffraction require working with the mathematics of Fresnel
Fresnel diffraction
In optics, the Fresnel diffraction equation for near-field diffraction, is an approximation of Kirchhoff-Fresnel diffraction that can be applied to the propagation of waves in the near field....
or Fraunhofer diffraction
Fraunhofer diffraction
In optics, the Fraunhofer diffraction equation is used to model the diffraction of waves when the diffraction pattern is viewed at a long distance from the diffracting object, and also when it is viewed at the focal plane of an imaging lens....
.
X-ray diffraction makes use of the fact that atoms in a crystal
Crystal
A crystal or crystalline solid is a solid material whose constituent atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions. The scientific study of crystals and crystal formation is known as crystallography...
have regular spacing at distances that are on the order of one angstrom
Ångström
The angstrom or ångström, is a unit of length equal to 1/10,000,000,000 of a meter . Its symbol is the Swedish letter Å....
. To see diffraction patterns, x-rays with similar wavelengths to that spacing are passed through the crystal. Since crystals are three-dimensional objects rather than two-dimensional gratings, the associated diffraction pattern varies in two directions according to Bragg reflection, with the associated bright spots occurring in unique patterns
Diffraction topography
Diffraction topography is an X-ray imaging technique based on Bragg diffraction.Diffraction topographic images record the intensity profile of a beam of X-rays diffracted by a crystal....
and
being twice the spacing between atoms.Diffraction effects limit the ability for an optical detector to optically resolve
Optical resolution
Optical resolution describes the ability of an imaging system to resolve detail in the object that is being imaged.An imaging system may have many individual components including a lens and recording and display components...
separate light sources. In general, light that is passing through an aperture
Aperture
In optics, an aperture is a hole or an opening through which light travels. More specifically, the aperture of an optical system is the opening that determines the cone angle of a bundle of rays that come to a focus in the image plane. The aperture determines how collimated the admitted rays are,...
will experience diffraction and the best images that can be created (as described in diffraction-limited optics) appear as a central spot with surrounding bright rings, separated by dark nulls; this pattern is known as an Airy pattern, and the central bright lobe as an Airy disk. The size of such a disk is given by
where θ is the angular resolution, λ is the wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
of the light, and D is the diameter
Diameter
In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints are on the circle. The diameters are the longest chords of the circle...
of the lens aperture. If the angular separation of the two points is significantly less than the Airy disk angular radius, then the two points cannot be resolved in the image, but if their angular separation is much greater than this, distinct images of the two points are formed and they can therefore be resolved. Rayleigh
John Strutt, 3rd Baron Rayleigh
John William Strutt, 3rd Baron Rayleigh, OM was an English physicist who, with William Ramsay, discovered the element argon, an achievement for which he earned the Nobel Prize for Physics in 1904...
defined the somewhat arbitrary "Rayleigh criterion" that two points whose angular separation is equal to the Airy disk radius (measured to first null, that is, to the first place where no light is seen) can be considered to be resolved. It can be seen that the greater the diameter of the lens or its aperture, the finer the resolution. Interferometry, with its ability to mimic extremely large baseline apertures, allows for the greatest angular resolution possible.
For astronomical imaging, the atmosphere prevents optimal resolution from being achieved in the visible spectrum due to the atmospheric scattering
Scattering
Scattering is a general physical process where some forms of radiation, such as light, sound, or moving particles, are forced to deviate from a straight trajectory by one or more localized non-uniformities in the medium through which they pass. In conventional use, this also includes deviation of...
and dispersion which cause stars to twinkle
Scintillation (astronomy)
Scintillation or twinkling are generic terms for rapid variations in apparent brightness or color of a distant luminous object viewed through a medium, most commonly the atmosphere ....
. Astronomers refer to this effect as the quality of astronomical seeing
Astronomical seeing
Astronomical seeing refers to the blurring and twinkling of astronomical objects such as stars caused by turbulent mixing in the Earth's atmosphere varying the optical refractive index...
. Techniques known as adaptive optics
Adaptive optics
Adaptive optics is a technology used to improve the performance of optical systems by reducing the effect of wavefront distortions. It is used in astronomical telescopes and laser communication systems to remove the effects of atmospheric distortion, and in retinal imaging systems to reduce the...
have been utilized to eliminate the atmospheric disruption of images and achieve results that approach the diffraction limit.
Dispersion and scattering
Thomson scattering
Thomson scattering is the elastic scattering of electromagnetic radiation by a free charged particle, as described by classical electromagnetism. It is just the low-energy limit of Compton scattering: the particle kinetic energy and photon frequency are the same before and after the scattering...
which occurs when electromagnetic waves are deflected by single particles. In the limit of Thompson scattering, in which the wavelike nature of light is evident, light is dispersed independent of the frequency, in contrast to Compton scattering
Compton scattering
In physics, Compton scattering is a type of scattering that X-rays and gamma rays undergo in matter. The inelastic scattering of photons in matter results in a decrease in energy of an X-ray or gamma ray photon, called the Compton effect...
which is frequency-dependent and strictly a quantum mechanical process, involving the nature of light as particles. In a statistical sense, elastic scattering of light by numerous particles much smaller than the wavelength of the light is a process known as Rayleigh scattering
Rayleigh scattering
Rayleigh scattering, named after the British physicist Lord Rayleigh, is the elastic scattering of light or other electromagnetic radiation by particles much smaller than the wavelength of the light. The particles may be individual atoms or molecules. It can occur when light travels through...
while the similar process for scattering by particles that are similar or larger in wavelength is known as Mie scattering with the Tyndall effect
Tyndall effect
The Tyndall effect, also known as Tyndall scattering, is light scattering by particles in a colloid or particles in a fine suspension. It is named after the 19th century physicist John Tyndall. It is similar to Rayleigh scattering, in that the intensity of the scattered light depends on the fourth...
being a commonly observed result. A small proportion of light scattering from atoms or molecules may undergo Raman scattering
Raman scattering
Raman scattering or the Raman effect is the inelastic scattering of a photon. It was discovered by Sir Chandrasekhara Venkata Raman and Kariamanickam Srinivasa Krishnan in liquids, and by Grigory Landsberg and Leonid Mandelstam in crystals....
, wherein the frequency changes due to excitation of the atoms and molecules. Brillouin scattering
Brillouin scattering
Brillouin scattering, named after Léon Brillouin, occurs when light in a medium interacts with time dependent optical density variations and changes its energy and path. The density variations may be due to acoustic modes, such as phonons, magnetic modes, such as magnons, or temperature gradients...
occurs when the frequency of light changes due to local changes with time and movements of a dense material.
Dispersion occurs when different frequencies of light have different phase velocities
Phase velocity
The phase velocity of a wave is the rate at which the phase of the wave propagates in space. This is the speed at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave will appear to travel at the phase velocity...
, due either to material properties (material dispersion) or to the geometry of an optical waveguide (waveguide dispersion). The most familiar form of dispersion is a decrease in index of refraction with increasing wavelength, which is seen in most transparent materials. This is called "normal dispersion". It occurs in all dielectric materials
Dielectric
A dielectric is an electrical insulator that can be polarized by an applied electric field. When a dielectric is placed in an electric field, electric charges do not flow through the material, as in a conductor, but only slightly shift from their average equilibrium positions causing dielectric...
, in wavelength ranges where the material does not absorb light. In wavelength ranges where a medium has significant absorption, the index of refraction can increase with wavelength. This is called "anomalous dispersion".
The separation of colors by a prism is an example of normal dispersion. At the surfaces of the prism, Snell's law predicts that light incident at an angle θ to the normal will be refracted at an angle arcsin(sin (θ) / n) . Thus, blue light, with its higher refractive index, is bent more strongly than red light, resulting in the well-known rainbow
Rainbow
A rainbow is an optical and meteorological phenomenon that causes a spectrum of light to appear in the sky when the Sun shines on to droplets of moisture in the Earth's atmosphere. It takes the form of a multicoloured arc...
pattern.
Abbe number
In physics and optics, the Abbe number, also known as the V-number or constringence of a transparent material, is a measure of the material's dispersion in relation to the refractive index...
, which gives a simple measure of dispersion based on the index of refraction at three specific wavelengths. Waveguide dispersion is dependent on the propagation constant
Propagation constant
The propagation constant of an electromagnetic wave is a measure of the change undergone by the amplitude of the wave as it propagates in a given direction. The quantity being measured can be the voltage or current in a circuit or a field vector such as electric field strength or flux density...
. Both kinds of dispersion cause changes in the group characteristics of the wave, the features of the wave packet that change with the same frequency as the amplitude of the electromagnetic wave. "Group velocity dispersion" manifests as a spreading-out of the signal "envelope" of the radiation and can be quantified with a group dispersion delay parameter:
where
is the group velocity. For a uniform medium, the group velocity iswhere n is the index of refraction and c is the speed of light in a vacuum. This gives a simpler form for the dispersion delay parameter:
If D is less than zero, the medium is said to have positive dispersion or normal dispersion. If D is greater than zero, the medium has negative dispersion. If a light pulse is propagated through a normally dispersive medium, the result is the higher frequency components slow down more than the lower frequency components. The pulse therefore becomes positively chirp
Chirp
A chirp is a signal in which the frequency increases or decreases with time. In some sources, the term chirp is used interchangeably with sweep signal. It is commonly used in sonar and radar, but has other applications, such as in spread spectrum communications...
ed, or up-chirped, increasing in frequency with time. This causes the spectrum coming out of a prism to appear with red light the least refracted and blue/violet light the most refracted. Conversely, if a pulse travels through an anomalously (negatively) dispersive medium, high frequency components travel faster than the lower ones, and the pulse becomes negatively chirped, or down-chirped, decreasing in frequency with time.
The result of group velocity dispersion, whether negative or positive, is ultimately temporal spreading of the pulse. This makes dispersion management extremely important in optical communications systems based on optical fiber
Optical fiber
An optical fiber is a flexible, transparent fiber made of a pure glass not much wider than a human hair. It functions as a waveguide, or "light pipe", to transmit light between the two ends of the fiber. The field of applied science and engineering concerned with the design and application of...
s, since if dispersion is too high, a group of pulses representing information will each spread in time and merge together, making it impossible to extract the signal.
Polarization
Polarization is a general property of waves that describes the orientation of their oscillations. For transverse waveTransverse wave
A transverse wave is a moving wave that consists of oscillations occurring perpendicular to the direction of energy transfer...
s such as many electromagnetic waves, it describes the orientation of the oscillations in the plane perpendicular to the wave's direction of travel. The oscillations may be oriented in a single direction (linear polarization
Linear polarization
In electrodynamics, linear polarization or plane polarization of electromagnetic radiation is a confinement of the electric field vector or magnetic field vector to a given plane along the direction of propagation...
), or the oscillation direction may rotate as the wave travels (circular
Circular polarization
In electrodynamics, circular polarization of an electromagnetic wave is a polarization in which the electric field of the passing wave does not change strength but only changes direction in a rotary type manner....
or elliptical polarization
Elliptical polarization
In electrodynamics, elliptical polarization is the polarization of electromagnetic radiation such that the tip of the electric field vector describes an ellipse in any fixed plane intersecting, and normal to, the direction of propagation...
). Circularly polarized waves can rotate rightward or leftward in the direction of travel, and which of those two rotations is present in a wave is called the wave's chirality
Polarimetry
Polarimetry is the measurement and interpretation of the polarization of transverse waves, most notably electromagnetic waves, such as radio or light waves...
.
The typical way to consider polarization is to keep track of the orientation of the electric field vector as the electromagnetic wave propagates. The electric field vector of a plane wave may be arbitrarily divided into two perpendicular components labeled x and y (with z indicating the direction of travel). The shape traced out in the x-y plane by the electric field vector is a Lissajous figure
Lissajous curve
In mathematics, a Lissajous curve , also known as Lissajous figure or Bowditch curve, is the graph of a system of parametric equationswhich describe complex harmonic motion...
that describes the polarization state. The following figures show some examples of the evolution of the electric field vector (blue), with time (the vertical axes), at a particular point in space, along with its x and y components (red/left and green/right), and the path traced by the vector in the plane (purple): The same evolution would occur when looking at the electric field at a particular time while evolving the point in space, along the direction opposite to propagation.
In the leftmost figure above, the x and y components of the light wave are in phase. In this case, the ratio of their strengths is constant, so the direction of the electric vector (the vector sum of these two components) is constant. Since the tip of the vector traces out a single line in the plane, this special case is called linear polarization
Linear polarization
In electrodynamics, linear polarization or plane polarization of electromagnetic radiation is a confinement of the electric field vector or magnetic field vector to a given plane along the direction of propagation...
. The direction of this line depends on the relative amplitudes of the two components.
In the middle figure, the two orthogonal components have the same amplitudes and are 90° out of phase. In this case, one component is zero when the other component is at maximum or minimum amplitude. There are two possible phase relationships that satisfy this requirement: the x component can be 90° ahead of the y component or it can be 90° behind the y component. In this special case, the electric vector traces out a circle in the plane, so this polarization is called circular polarization. The rotation direction in the circle depends on which of the two phase relationships exists and corresponds to right-hand circular polarization and left-hand circular polarization.
In all other cases, where the two components either do not have the same amplitudes and/or their phase difference is neither zero nor a multiple of 90°, the polarization is called elliptical polarization
Elliptical polarization
In electrodynamics, elliptical polarization is the polarization of electromagnetic radiation such that the tip of the electric field vector describes an ellipse in any fixed plane intersecting, and normal to, the direction of propagation...
because the electric vector traces out an ellipse
Ellipse
In geometry, an ellipse is a plane curve that results from the intersection of a cone by a plane in a way that produces a closed curve. Circles are special cases of ellipses, obtained when the cutting plane is orthogonal to the cone's axis...
in the plane (the polarization ellipse). This is shown in the above figure on the right. Detailed mathematics of polarization is done using Jones calculus
Jones calculus
In optics, polarized light can be described using the Jones calculus, invented by R. C. Jones in 1941. Polarized light is represented by a Jones vector, and linear optical elements are represented by Jones matrices...
and is characterized by the Stokes parameters
Stokes parameters
The Stokes parameters are a set of values that describe the polarization state of electromagnetic radiation. They were defined by George Gabriel Stokes in 1852, as a mathematically convenient alternative to the more common description of incoherent or partially polarized radiation in terms of its...
.
Media that have different indexes of refraction for different polarization modes are called birefringent
Birefringence
Birefringence, or double refraction, is the decomposition of a ray of light into two rays when it passes through certain anisotropic materials, such as crystals of calcite or boron nitride. The effect was first described by the Danish scientist Rasmus Bartholin in 1669, who saw it in calcite...
. Well known manifestations of this effect appear in optical wave plate
Wave plate
A wave plate or retarder is an optical device that alters the polarization state of a light wave travelling through it.- Operation :A wave plate works by shifting the phase between two perpendicular polarization components of the light wave. A typical wave plate is simply a birefringent crystal...
s/retarders (linear modes) and in Faraday rotation/optical rotation
Optical rotation
Optical rotation is the turning of the plane of linearly polarized light about the direction of motion as the light travels through certain materials. It occurs in solutions of chiral molecules such as sucrose , solids with rotated crystal planes such as quartz, and spin-polarized gases of atoms...
(circular modes). If the path length in the birefringent medium is sufficient, plane waves will exit the material with a significantly different propagation direction, due to refraction
Refraction
Refraction is the change in direction of a wave due to a change in its speed. It is essentially a surface phenomenon . The phenomenon is mainly in governance to the law of conservation of energy. The proper explanation would be that due to change of medium, the phase velocity of the wave is changed...
. For example, this is the case with macroscopic crystals of calcite
Calcite
Calcite is a carbonate mineral and the most stable polymorph of calcium carbonate . The other polymorphs are the minerals aragonite and vaterite. Aragonite will change to calcite at 380-470°C, and vaterite is even less stable.-Properties:...
, which present the viewer with two offset, orthogonally polarized images of whatever is viewed through them. It was this effect that provided the first discovery of polarization, by Erasmus Bartholinus in 1669. In addition, the phase shift, and thus the change in polarization state, is usually frequency dependent, which, in combination with dichroism
Dichroism
Dichroism has two related but distinct meanings in optics. A dichroic material is either one which causes visible light to be split up into distinct beams of different wavelengths , or one in which light rays having different polarizations are absorbed by different amounts.The original meaning of...
, often gives rise to bright colors and rainbow-like effects. In mineralogy
Mineralogy
Mineralogy is the study of chemistry, crystal structure, and physical properties of minerals. Specific studies within mineralogy include the processes of mineral origin and formation, classification of minerals, their geographical distribution, as well as their utilization.-History:Early writing...
, such properties, known as pleochroism
Pleochroism
Pleochroism is an optical phenomenon in which a substance appears to be different colors when observed at different angles with polarized light.- Background :Anisotropic crystals will have optical properties that vary with the direction of light...
, are frequently exploited for the purpose of identifying minerals using polarization microscope
Microscope
A microscope is an instrument used to see objects that are too small for the naked eye. The science of investigating small objects using such an instrument is called microscopy...
s. Additionally, many plastics that are not normally birefringent will become so when subject to mechanical stress, a phenomenon which is the basis of photoelasticity
Photoelasticity
Photoelasticity is an experimental method to determine the stress distribution in a material. The method is mostly used in cases where mathematical methods become quite cumbersome. Unlike the analytical methods of stress determination, photoelasticity gives a fairly accurate picture of stress...
. Non-birefringent methods, to rotate the linear polarization of light beams, include the use of prismatic polarization rotator
Polarization rotator
A polarization rotator is an optical device that rotates the polarization axis of a linearly polarized light beam by an angle of choice. These rotators are either based on the principle of birefringence or on total internal reflection....
s which utilize total internal reflection
Total internal reflection
Total internal reflection is an optical phenomenon that happens when a ray of light strikes a medium boundary at an angle larger than a particular critical angle with respect to the normal to the surface. If the refractive index is lower on the other side of the boundary and the incident angle is...
in a prism set designed for efficient colinear transmission.
Dichroism
Dichroism has two related but distinct meanings in optics. A dichroic material is either one which causes visible light to be split up into distinct beams of different wavelengths , or one in which light rays having different polarizations are absorbed by different amounts.The original meaning of...
. with devices that block nearly all of the radiation in one mode known as polarizing filters or simply "polarizer
Polarizer
A polarizer is an optical filter that passes light of a specific polarization and blocks waves of other polarizations. It can convert a beam of light of undefined or mixed polarization into a beam with well-defined polarization. The common types of polarizers are linear polarizers and circular...
s". Malus' law, which is named after Etienne-Louis Malus
Étienne-Louis Malus
- External links :...
, says that when a perfect polarizer is placed in a linear polarized beam of light, the intensity, I, of the light that passes through is given by
where
- I0 is the initial intensity,
- and θi is the angle between the light's initial polarization direction and the axis of the polarizer.
A beam of unpolarized light can be thought of as containing a uniform mixture of linear polarizations at all possible angles. Since the average value of
is 1/2, the transmission coefficient becomesIn practice, some light is lost in the polarizer and the actual transmission of unpolarized light will be somewhat lower than this, around 38% for Polaroid-type polarizers but considerably higher (>49.9%) for some birefringent prism types.
In addition to birefringence and dichroism in extended media, polarization effects can also occur at the (reflective) interface between two materials of different refractive index. These effects are treated by the Fresnel equations
Fresnel equations
The Fresnel equations , deduced by Augustin-Jean Fresnel , describe the behaviour of light when moving between media of differing refractive indices...
. Part of the wave is transmitted and part is reflected, with the ratio depending on angle of incidence and the angle of refraction. In this way, physical optics recovers Brewster's angle
Brewster's angle
Brewster's angle is an angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface, with no reflection. When unpolarized light is incident at this angle, the light that is reflected from the surface is therefore perfectly...
.
Electromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...
contain a large number of atoms or molecules that emit light. The orientation of the electric fields produced by these emitters may not be correlated, in which case the light is said to be unpolarized. If there is partial correlation between the emitters, the light is partially polarized. If the polarization is consistent across the spectrum of the source, partially polarized light can be described as a superposition of a completely unpolarized component, and a completely polarized one. One may then describe the light in terms of the degree of polarization
Degree of polarization
Degree of polarization is a quantity used to describe the portion of an electromagnetic wave which is polarized. A perfectly polarized wave has a DOP of 100%, whereas an unpolarized wave has a DOP of 0%. A wave which is partially polarized, and therefore can be represented by a superposition of...
, and the parameters of the polarization ellipse.
Light reflected by shiny transparent materials is partly or fully polarized, except when the light is normal (perpendicular) to the surface. It was this effect that allowed the mathematician Etienne Louis Malus to make the measurements that allowed for his development of the first mathematical models for polarized light. Polarization occurs when light is scattered in the atmosphere
Earth's atmosphere
The atmosphere of Earth is a layer of gases surrounding the planet Earth that is retained by Earth's gravity. The atmosphere protects life on Earth by absorbing ultraviolet solar radiation, warming the surface through heat retention , and reducing temperature extremes between day and night...
. The scattered light produces the brightness and color in clear skies
Sky
The sky is the part of the atmosphere or outer space visible from the surface of any astronomical object. It is difficult to define precisely for several reasons. During daylight, the sky of Earth has the appearance of a pale blue surface because the air scatters the sunlight. The sky is sometimes...
. This partial polarization of scattered light can be taken advantage of using polarizing filters to darken the sky in photographs
Science of photography
The science of photography refers to the use of science, such as chemistry and physics, in all aspects of photography. This applies to the camera, its lenses, physical operation of the camera, electronic camera internals, and the process of developing film in order to take and develop pictures...
. Optical polarization is principally of importance in chemistry
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....
due to circular dichroism
Circular dichroism
Circular dichroism refers to the differential absorption of left and right circularly polarized light. This phenomenon was discovered by Jean-Baptiste Biot, Augustin Fresnel, and Aimé Cotton in the first half of the 19th century. It is exhibited in the absorption bands of optically active chiral...
and optical rotation
Optical rotation
Optical rotation is the turning of the plane of linearly polarized light about the direction of motion as the light travels through certain materials. It occurs in solutions of chiral molecules such as sucrose , solids with rotated crystal planes such as quartz, and spin-polarized gases of atoms...
("circular birefringence") exhibited by optically active (chiral
Chirality (chemistry)
A chiral molecule is a type of molecule that lacks an internal plane of symmetry and thus has a non-superimposable mirror image. The feature that is most often the cause of chirality in molecules is the presence of an asymmetric carbon atom....
) molecules.
Modern optics
Modern optics encompasses the areas of optical science and engineering that became popular in the 20th century. These areas of optical science typically relate to the electromagnetic or quantum properties of light but do include other topics. A major subfield of modern optics, quantum opticsQuantum optics
Quantum optics is a field of research in physics, dealing with the application of quantum mechanics to phenomena involving light and its interactions with matter.- History of quantum optics :...
, deals with specifically quantum mechanical properties of light. Quantum optics is not just theoretical; some modern devices, such as lasers, have principles of operation that depend on quantum mechanics. Light detectors, such as photomultiplier
Photomultiplier
Photomultiplier tubes , members of the class of vacuum tubes, and more specifically phototubes, are extremely sensitive detectors of light in the ultraviolet, visible, and near-infrared ranges of the electromagnetic spectrum...
s and channeltrons, respond to individual photons. Electronic image sensor
Image sensor
An image sensor is a device that converts an optical image into an electronic signal. It is used mostly in digital cameras and other imaging devices...
s, such as CCDs
Charge-coupled device
A charge-coupled device is a device for the movement of electrical charge, usually from within the device to an area where the charge can be manipulated, for example conversion into a digital value. This is achieved by "shifting" the signals between stages within the device one at a time...
, exhibit shot noise
Shot noise
Shot noise is a type of electronic noise that may be dominant when the finite number of particles that carry energy is sufficiently small so that uncertainties due to the Poisson distribution, which describes the occurrence of independent random events, are of significance...
corresponding to the statistics of individual photon events. Light-emitting diode
Light-emitting diode
A light-emitting diode is a semiconductor light source. LEDs are used as indicator lamps in many devices and are increasingly used for other lighting...
s and photovoltaic cells, too, cannot be understood without quantum mechanics. In the study of these devices, quantum optics often overlaps with quantum electronics.
Specialty areas of optics research include the study of how light interacts with specific materials as in crystal optics
Crystal optics
Crystal optics is the branch of optics that describes the behaviour of light in anisotropic media, that is, media in which light behaves differently depending on which direction the light is propagating. The index of refraction depends on both composition and crystal structure and can be...
and metamaterial
Metamaterial
Metamaterials are artificial materials engineered to have properties that may not be found in nature. Metamaterials usually gain their properties from structure rather than composition, using small inhomogeneities to create effective macroscopic behavior....
s. Other research focuses on the phenomenology of electromagnetic waves as in singular optics
Optical vortex
An optical vortex is a zero of an optical field, a point of zero intensity. Research into the properties of vortices has thrived since a comprehensive paper by Nye and Berry, in 1974, described the basic properties of "dislocations in wave trains"...
, non-imaging optics, non-linear optics, statistical optics, and radiometry
Radiometry
In optics, radiometry is a set of techniques for measuring electromagnetic radiation, including visible light. Radiometric techniques characterize the distribution of the radiation's power in space, as opposed to photometric techniques, which characterize the light's interaction with the human eye...
. Additionally, computer engineers have taken an interest in integrated optics, machine vision
Machine vision
Machine vision is the process of applying a range of technologies and methods to provide imaging-based automatic inspection, process control and robot guidance in industrial applications. While the scope of MV is broad and a comprehensive definition is difficult to distil, a "generally accepted...
, and photonic computing
Photonic computing
Today's computers use the movement of electrons in-and-out of transistors to do logic. Optical or Photonic computing is intended to use photons or light particles, produced by lasers or diodes, in place of electrons...
as possible components of the "next generation" of computers.
Today, the pure science of optics is called optical science or optical physics
Optical physics
Optical physics, or optical science, is a subfield of atomic, molecular, and optical physics. It is the study of the generation of electromagnetic radiation, the properties of that radiation, and the interaction of that radiation with matter, especially its manipulation and control...
to distinguish it from applied optical sciences, which are referred to as optical engineering
Optical engineering
Optical engineering is the field of study that focuses on applications of optics. Optical engineers design components of optical instruments such as lenses, microscopes, telescopes, and other equipment that utilizes the properties of light. Other devices include optical sensors and measurement...
. Prominent subfields of optical engineering include illumination engineering
Lighting
Lighting or illumination is the deliberate application of light to achieve some practical or aesthetic effect. Lighting includes the use of both artificial light sources such as lamps and light fixtures, as well as natural illumination by capturing daylight...
, photonics
Photonics
The science of photonics includes the generation, emission, transmission, modulation, signal processing, switching, amplification, detection and sensing of light. The term photonics thereby emphasizes that photons are neither particles nor waves — they are different in that they have both particle...
, and optoelectronics
Optoelectronics
Optoelectronics is the study and application of electronic devices that source, detect and control light, usually considered a sub-field of photonics. In this context, light often includes invisible forms of radiation such as gamma rays, X-rays, ultraviolet and infrared, in addition to visible light...
with practical applications like lens design
Optical lens design
Optical lens design refers to the calculation of lens construction parameters that will meet a set of performance requirements and constraints, including cost and schedule limitations....
, fabrication and testing of optical components
Fabrication and testing (optical components)
Optical fabrication and testing spans an enormous range of manufacturing procedures and optical test configurations.The manufacture of a conventional spherical lens typically begins with the generation of the optic's rough shape by grinding a glass blank. This can be done, for example, with ring...
, and image processing
Image processing
In electrical engineering and computer science, image processing is any form of signal processing for which the input is an image, such as a photograph or video frame; the output of image processing may be either an image or, a set of characteristics or parameters related to the image...
. Some of these fields overlap, with nebulous boundaries between the subjects terms that mean slightly different things in different parts of the world and in different areas of industry. A professional community of researchers in nonlinear optics has developed in the last several decades due to advances in laser technology
Laser
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of photons. The term "laser" originated as an acronym for Light Amplification by Stimulated Emission of Radiation...
.
Lasers
Stimulated emission
In optics, stimulated emission is the process by which an atomic electron interacting with an electromagnetic wave of a certain frequency may drop to a lower energy level, transferring its energy to that field. A photon created in this manner has the same phase, frequency, polarization, and...
. The term laser is an acronym for Light Amplification by Stimulated Emission of Radiation. Laser light is usually spatially coherent
Coherence (physics)
In physics, coherence is a property of waves that enables stationary interference. More generally, coherence describes all properties of the correlation between physical quantities of a wave....
, which means that the light either is emitted in a narrow, low-divergence beam
Beam divergence
The beam divergence of an electromagnetic beam is an angular measure of the increase in beam diameter or radius with distance from the optical aperture or antenna aperture from which the electromagnetic beam emerges. The term is relevant only in the "far field", away from any focus of the beam...
, or can be converted into one with the help of optical components such as lens
Lens (optics)
A lens is an optical device with perfect or approximate axial symmetry which transmits and refracts light, converging or diverging the beam. A simple lens consists of a single optical element...
es. Because the microwave
Microwave
Microwaves, a subset of radio waves, have wavelengths ranging from as long as one meter to as short as one millimeter, or equivalently, with frequencies between 300 MHz and 300 GHz. This broad definition includes both UHF and EHF , and various sources use different boundaries...
equivalent of the laser, the maser, was developed first, devices that emit microwave and radio
Radio frequency
Radio frequency is a rate of oscillation in the range of about 3 kHz to 300 GHz, which corresponds to the frequency of radio waves, and the alternating currents which carry radio signals...
frequencies are usually called masers.
The first working laser was demonstrated on 16 May 1960 by Theodore Maiman at Hughes Research Laboratories
Hughes Research Laboratories
HRL Laboratories , was the research arm of the Hughes Aircraft Company. Its dedicated research center was established in 1960 in Malibu...
. When first invented, they were called "a solution looking for a problem". Since then, lasers have become a multi-billion dollar industry, finding utility in thousands of highly varied applications. The first application of lasers visible in the daily lives of the general population was the supermarket barcode
Barcode
A barcode is an optical machine-readable representation of data, which shows data about the object to which it attaches. Originally barcodes represented data by varying the widths and spacings of parallel lines, and may be referred to as linear or 1 dimensional . Later they evolved into rectangles,...
scanner, introduced in 1974. The laserdisc
Laserdisc
LaserDisc was a home video format and the first commercial optical disc storage medium. Initially licensed, sold, and marketed as MCA DiscoVision in North America in 1978, the technology was previously referred to interally as Optical Videodisc System, Reflective Optical Videodisc, Laser Optical...
player, introduced in 1978, was the first successful consumer product to include a laser, but the compact disc
Compact Disc
The Compact Disc is an optical disc used to store digital data. It was originally developed to store and playback sound recordings exclusively, but later expanded to encompass data storage , write-once audio and data storage , rewritable media , Video Compact Discs , Super Video Compact Discs ,...
player was the first laser-equipped device to become truly common in consumers' homes, beginning in 1982. These optical storage
Optical storage
Optical storage is a term from engineering referring to the storage of data on an optically readable medium. Data is recorded by making marks in a pattern that can be read back with the aid of light, usually a beam of laser light precisely focused on a spinning disc. An older example, that does...
devices use a semiconductor laser less than a millimeter wide to scan the surface of the disc for data retrieval. Fiber-optic communication
Fiber-optic communication
Fiber-optic communication is a method of transmitting information from one place to another by sending pulses of light through an optical fiber. The light forms an electromagnetic carrier wave that is modulated to carry information...
relies on lasers to transmit large amounts of information at the speed of light. Other common applications of lasers include laser printers and laser pointer
Laser pointer
A laser pointer or laser pen is a small portable device with a power source and a laser emitting a very narrow coherent low-powered beam of visible light, intended to be used to highlight something of interest by illuminating it with a small bright spot of colored light...
s. Lasers are used in medicine in areas such as bloodless surgery
Bloodless surgery
Bloodless surgery is a term that was popularized at the beginning of the 20th century by the practice of an internationally famous orthopedic surgeon, Adolf Lorenz, who was known as "the bloodless surgeon of Vienna." This expression reflected Lorenz's methods for treating patients with noninvasive...
, laser eye surgery, and laser capture microdissection
Laser capture microdissection
Laser capture microdissection , also called Microdissection, Laser MicroDissection , or Laser-assisted microdissection is a method for isolating specific cells of interest from microscopic regions of tissue/cells/organisms....
and in military applications such as missile defense systems, electro-optical countermeasures (EOCM), and LIDAR
LIDAR
LIDAR is an optical remote sensing technology that can measure the distance to, or other properties of a target by illuminating the target with light, often using pulses from a laser...
. Lasers are also used in holograms, bubblegram
Bubblegram
A bubblegram is a 3D image composed of points suspended in a medium, typically a plastic block. It can be described as a 3D version of the late 19th century, European, 2D art of pointillism....
s, laser light shows
Laser lighting display
A laser lighting display or laser light show involves the use of laser light to entertain an audience. A laser light show may consist only of projected laser beams set to music, or may accompany another form of entertainment, typically a dance concert or other musical performance.Laser light is...
, and laser hair removal
Laser hair removal
Laser hair removal was performed experimentally for about 20 years before it became commercially available in the mid 1990s. One of the first published articles describing laser hair removal was authored by the group at Massachusetts General Hospital in 1998...
.
Applications
Optics is part of everyday life. The ubiquity of visual systemVisual system
The visual system is the part of the central nervous system which enables organisms to process visual detail, as well as enabling several non-image forming photoresponse functions. It interprets information from visible light to build a representation of the surrounding world...
s in biology indicate the central role optics plays as the science of one of the five senses
Sense
Senses are physiological capacities of organisms that provide inputs for perception. The senses and their operation, classification, and theory are overlapping topics studied by a variety of fields, most notably neuroscience, cognitive psychology , and philosophy of perception...
. Many people benefit from eyeglasses or contact lenses, and optics are integral to the functioning of many consumer goods including cameras. Rainbows and mirage
Mirage
A mirage is a naturally occurring optical phenomenon in which light rays are bent to produce a displaced image of distant objects or the sky. The word comes to English via the French mirage, from the Latin mirare, meaning "to look at, to wonder at"...
s are examples of optical phenomena. Optical communication
Optical communication
Optical communication is any form of telecommunication that uses light as the transmission medium.An optical communication system consists of a transmitter, which encodes a message into an optical signal, a channel, which carries the signal to its destination, and a receiver, which reproduces the...
provides the backbone for both the Internet
Internet
The Internet is a global system of interconnected computer networks that use the standard Internet protocol suite to serve billions of users worldwide...
and modern telephony
Telephony
In telecommunications, telephony encompasses the general use of equipment to provide communication over distances, specifically by connecting telephones to each other....
.
Human eye
Retina
The vertebrate retina is a light-sensitive tissue lining the inner surface of the eye. The optics of the eye create an image of the visual world on the retina, which serves much the same function as the film in a camera. Light striking the retina initiates a cascade of chemical and electrical...
, which covers the back of the eye. The focusing is accomplished by a series of transparent media. Light entering the eye passes first through the cornea
Cornea
The cornea is the transparent front part of the eye that covers the iris, pupil, and anterior chamber. Together with the lens, the cornea refracts light, with the cornea accounting for approximately two-thirds of the eye's total optical power. In humans, the refractive power of the cornea is...
, which provides much of the eye's optical power. The light then continues through the fluid just behind the cornea—the anterior chamber
Anterior chamber
The anterior chamber is the fluid-filled space inside the eye between the iris and the cornea's innermost surface, the endothelium. Aqueous humor is the fluid that fills the anterior chamber. Hyphema and glaucoma are two main pathologies in this area. In hyphema, blood fills the anterior chamber...
, then passes through the pupil
Pupil
The pupil is a hole located in the center of the iris of the eye that allows light to enter the retina. It appears black because most of the light entering the pupil is absorbed by the tissues inside the eye. In humans the pupil is round, but other species, such as some cats, have slit pupils. In...
. The light then passes through the lens
Lens (anatomy)
The crystalline lens is a transparent, biconvex structure in the eye that, along with the cornea, helps to refract light to be focused on the retina. The lens, by changing shape, functions to change the focal distance of the eye so that it can focus on objects at various distances, thus allowing a...
, which focuses the light further and allows adjustment of focus. The light then passes through the main body of fluid in the eye—the vitreous humor, and reaches the retina. The cells in the retina cover the back of the eye, except for where the optic nerve
Optic nerve
The optic nerve, also called cranial nerve 2, transmits visual information from the retina to the brain. Derived from the embryonic retinal ganglion cell, a diverticulum located in the diencephalon, the optic nerve doesn't regenerate after transection.-Anatomy:The optic nerve is the second of...
exits; this results in a blind spot
Blind spot (vision)
A blind spot, also known as a scotoma, is an obscuration of the visual field. A particular blind spot known as the blindspot, or physiological blind spot, or punctum caecum in medical literature, is the place in the visual field that corresponds to the lack of light-detecting photoreceptor cells on...
.
There are two types of photoreceptor cells, rods and cones, which are sensitive to different aspects of light. Rod cells are sensitive to the intensity of light over a wide frequency range, thus are responsible for black-and-white vision
Scotopic vision
Scotopic vision is the vision of the eye under low light conditions. The term comes from Greek skotos meaning darkness and -opia meaning a condition of sight...
. Rod cells are not present on the fovea
Fovea
The fovea centralis, also generally known as the fovea , is a part of the eye, located in the center of the macula region of the retina....
, the area of the retina responsible for central vision, and are not as responsive as cone cells to spatial and temporal changes in light. There are, however, twenty times more rod cells than cone cells in the retina because the rod cells are present across a wider area. Because of their wider distribution, rods are responsible for peripheral vision
Peripheral vision
Peripheral vision is a part of vision that occurs outside the very center of gaze. There is a broad set of non-central points in the field of view that is included in the notion of peripheral vision...
.
In contrast, cone cells are less sensitive to the overall intensity of light, but come in three varieties that are sensitive to different frequency-ranges and thus are used in the perception of color
Color
Color or colour is the visual perceptual property corresponding in humans to the categories called red, green, blue and others. Color derives from the spectrum of light interacting in the eye with the spectral sensitivities of the light receptors...
and photopic vision
Photopic vision
Photopic vision is the vision of the eye under well-lit conditions. In humans and many other animals, photopic vision allows color perception, mediated by cone cells, and a significantly higher visual acuity and temporal resolution than available with scotopic vision.The human eye uses three types...
. Cone cells are highly concentrated in the fovea and have a high visual acuity meaning that they are better at spatial resolution than rod cells. Since cone cells are not as sensitive to dim light as rod cells, most night vision
Night vision
Night vision is the ability to see in low light conditions. Whether by biological or technological means, night vision is made possible by a combination of two approaches: sufficient spectral range, and sufficient intensity range...
is limited to rod cells. Likewise, since cone cells are in the fovea, central vision (including the vision needed to do most reading, fine detail work such as sewing, or careful examination of objects) is done by cone cells.
Ciliary muscle
Ciliary muscle
The ciliary muscle is a ring of striated smooth muscle in the eye's middle layer that controls accommodation for viewing objects at varying distances and regulates the flow of aqueous humour into Schlemm's canal. It changes the shape of the lens within the eye not the size of the pupil which is...
s around the lens allow the eye's focus to be adjusted. This process is known as accommodation
Accommodation (eye)
Accommodation is the process by which the vertebrate eye changes optical power to maintain a clear image on an object as its distance changes....
. The near point and far point
Far point
In visual perception, the far point is the point at which an object must be placed along the optical axis for its image to be focused on the retina when the eye is not accommodating...
define the nearest and farthest distances from the eye at which an object can be brought into sharp focus. For a person with normal vision, the far point is located at infinity. The near point's location depends on how much the muscles can increase the curvature of the lens, and how inflexible the lens has become with age. Optometrists, ophthalmologists, and optician
Optician
An optician is a person who is trained to fill prescriptions for eye correction in the field of medicine, also known as a dispensing optician or optician, dispensing...
s usually consider an appropriate near point to be closer than normal reading distance—approximately 25 cm.
Defects in vision can be explained using optical principles. As people age, the lens becomes less flexible and the near point recedes from the eye, a condition known as presbyopia
Presbyopia
Presbyopia is a condition where the eye exhibits a progressively diminished ability to focus on near objects with age. Presbyopia’s exact mechanisms are not known with certainty; the research evidence most strongly supports a loss of elasticity of the crystalline lens, although changes in the...
. Similarly, people suffering from hyperopia
Hyperopia
Hyperopia, also known as farsightedness, longsightedness or hypermetropia, is a defect of vision caused by an imperfection in the eye , causing difficulty focusing on near objects, and in extreme cases causing a sufferer to be unable to focus on objects at any distance...
cannot decrease the focal length of their lens enough to allow for nearby objects to be imaged on their retina. Conversely, people who cannot increase the focal length of their lens enough to allow for distant objects to be imaged on the retina suffer from myopia
Myopia
Myopia , "shortsightedness" ) is a refractive defect of the eye in which collimated light produces image focus in front of the retina under conditions of accommodation. In simpler terms, myopia is a condition of the eye where the light that comes in does not directly focus on the retina but in...
and have a far point that is considerably closer than infinity. A condition known as astigmatism
Astigmatism
An optical system with astigmatism is one where rays that propagate in two perpendicular planes have different foci. If an optical system with astigmatism is used to form an image of a cross, the vertical and horizontal lines will be in sharp focus at two different distances...
results when the cornea is not spherical but instead is more curved in one direction. This causes horizontally extended objects to be focused on different parts of the retina than vertically extended objects, and results in distorted images.
All of these conditions can be corrected using corrective lens
Corrective lens
A corrective lens is a lens worn in front of the eye, mainly used to treat myopia, hyperopia, astigmatism, and presbyopia. Glasses or "spectacles" are worn on the face a short distance in front of the eye. Contact lenses are worn directly on the surface of the eye...
es. For presbyopia and hyperopia, a converging lens provides the extra curvature necessary to bring the near point closer to the eye while for myopia a diverging lens provides the curvature necessary to send the far point to infinity. Astigmatism is corrected with a cylindrical surface
Cylinder (geometry)
A cylinder is one of the most basic curvilinear geometric shapes, the surface formed by the points at a fixed distance from a given line segment, the axis of the cylinder. The solid enclosed by this surface and by two planes perpendicular to the axis is also called a cylinder...
lens that curves more strongly in one direction than in another, compensating for the non-uniformity of the cornea.
The optical power of corrective lenses is measured in diopters, a value equal to the reciprocal
Multiplicative inverse
In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a/b is b/a. For the multiplicative inverse of a real number, divide 1 by the...
of the focal length measured in meters; with a positive focal length corresponding to a converging lens and a negative focal length corresponding to a diverging lens. For lenses that correct for astigmatism as well, three numbers are given: one for the spherical power, one for the cylindrical power, and one for the angle of orientation of the astigmatism.
Visual effects
Visual perception
Visual perception is the ability to interpret information and surroundings from the effects of visible light reaching the eye. The resulting perception is also known as eyesight, sight, or vision...
images that differ from objective reality. The information gathered by the eye is processed in the brain to give a percept that differs from the object being imaged. Optical illusions can be the result of a variety of phenomena including physical effects that create images that are different from the objects that make them, the physiological effects on the eyes and brain of excessive stimulation (e.g. brightness, tilt, color, movement), and cognitive illusions where the eye and brain make unconscious inferences.
Cognitive illusions include some which result from the unconscious misapplication of certain optical principles. For example, the Ames room
Ames room
An Ames room is a distorted room that is used to create an optical illusion. Probably influenced by the writings of Hermann Helmholtz, it was invented by American ophthalmologist Adelbert Ames, Jr...
, Hering
Hering illusion
The Hering illusion is a one of the geometrical-optical illusions and was discovered by the German physiologist Ewald Hering in 1861 . Two straight and parallel lines look as if they were bowed outwards. The distortion is produced by the radiating pattern and was ascribed by Hering to an...
, Müller-Lyer, Orbison, Ponzo
Ponzo illusion
The Ponzo illusion is a geometrical-optical illusion that was first demonstrated by the Italian psychologist Mario Ponzo in 1913. He suggested that the human mind judges an object's size based on its background. He showed this by drawing two identical lines across a pair of converging lines,...
, Sander
Sander illusion
The Sander illusion or Sander's parallelogram is an optical illusion described by the German psychologist Friedrich Sander in 1926...
, and Wundt illusion
Wundt illusion
The Wundt illusion is an optical illusion that was first described by the German psychologist Wilhelm Wundt in the 19th century. The two red vertical lines are both straight, but they may look as if they are bowed inwards to some observers. The distortion is induced by the crooked lines on the...
s all rely on the suggestion of the appearance of distance by using converging and diverging lines, in the same way that parallel light rays (or indeed any set of parallel lines) appear to converge at a vanishing point
Vanishing point
A vanishing point is a point in a perspective drawing to which parallel lines not parallel to the image plane appear to converge. The number and placement of the vanishing points determines which perspective technique is being used...
at infinity in two-dimensionally rendered images with artistic perspective
Perspective (graphical)
Perspective in the graphic arts, such as drawing, is an approximate representation, on a flat surface , of an image as it is seen by the eye...
. This suggestion is also responsible for the famous moon illusion
Moon illusion
The Moon illusion is an optical illusion in which the Moon appears larger near the horizon than it does while higher up in the sky. This optical illusion also occurs with the sun and star constellations. It has been known since ancient times, and recorded by numerous different cultures...
where the moon, despite having essentially the same angular size, appears much larger near the horizon
Horizon
The horizon is the apparent line that separates earth from sky, the line that divides all visible directions into two categories: those that intersect the Earth's surface, and those that do not. At many locations, the true horizon is obscured by trees, buildings, mountains, etc., and the resulting...
than it does at zenith
Zenith
The zenith is an imaginary point directly "above" a particular location, on the imaginary celestial sphere. "Above" means in the vertical direction opposite to the apparent gravitational force at that location. The opposite direction, i.e...
. This illusion so confounded Ptolemy that he incorrectly attributed it to atmospheric refraction when he described it in his treatise, Optics.
Another type of optical illusion exploits broken patterns to trick the mind into perceiving symmetries or asymmetries that are not present. Examples include the café wall
Café wall illusion
The café wall illusion is a geometrical-optical illusion in which the parallel straight dividing lines between staggered rows with alternating black and white "bricks" appear to be sloped....
, Ehrenstein
Ehrenstein illusion
The Ehrenstein illusion is an optical illusion studied by the German psychologist Walter Ehrenstein in which the sides of a square placed inside a pattern of concentric circles take an apparent curved shape ....
, Fraser spiral
Fraser spiral illusion
The Fraser spiral illusion is an optical illusion that was first described by the British psychologist James Fraser in 1908.The illusion is also known as the false spiral, or by its original name, the twisted cord illusion...
, Poggendorff
Poggendorff illusion
The Poggendorff Illusion is a geometrical-optical illusion that involves the misperception of the position of one segment of a transverse line that has been interrupted by the contour of an intervening structure...
, and Zöllner illusion
Zollner illusion
The Zöllner illusion is a classic optical illusion named after its discoverer, German astrophysicist Johann Karl Friedrich Zöllner. In 1860, Zöllner sent his discovery in a letter to physicist and scholar Johann Christian Poggendorff, editor of Annalen der Physik und Chemie, who subsequently...
s. Related, but not strictly illusions, are patterns that occur due to the superimposition of periodic structures. For example transparent tissues with a grid structure produce shapes known as moiré pattern
Moiré pattern
In physics, a moiré pattern is an interference pattern created, for example, when two grids are overlaid at an angle, or when they have slightly different mesh sizes.- Etymology :...
s, while the superimposition of periodic transparent patterns comprising parallel opaque lines or curves produces line moiré
Line moiré
Line moiré is one type of moiré pattern; a pattern that appears when superposing two transparent layers containing correlated opaque patterns. Line moiré is the case when the superposed patterns comprise straight or curved lines. When moving the layer patterns, the moiré patterns transform or move...
patterns.
Optical instruments
Photographic lens
A camera lens is an optical lens or assembly of lenses used in conjunction with a camera body and mechanism to make images of objects either on photographic film or on other media capable of storing an image chemically or electronically.While in principle a simple convex lens will suffice, in...
es, corrective lenses, and magnifying glass
Magnifying glass
A magnifying glass is a convex lens that is used to produce a magnified image of an object. The lens is usually mounted in a frame with a handle ....
es while single mirrors are used in parabolic reflector
Parabolic reflector
A parabolic reflector is a reflective device used to collect or project energy such as light, sound, or radio waves. Its shape is that of a circular paraboloid, that is, the surface generated by a parabola revolving around its axis...
s and rear-view mirror
Rear-view mirror
A rear-view mirror is a mirror in automobiles and other vehicles, designed to allow the driver to see rearward through the vehicle's backlight ....
s. Combining a number of mirrors, prisms, and lenses produces compound optical instruments which have practical uses. For example, a periscope
Periscope
A periscope is an instrument for observation from a concealed position. In its simplest form it consists of a tube with mirrors at each end set parallel to each other at a 45-degree angle....
is simply two plane mirrors aligned to allow for viewing around obstructions. The most famous compound optical instruments in science are the microscope
Optical microscope
The optical microscope, often referred to as the "light microscope", is a type of microscope which uses visible light and a system of lenses to magnify images of small samples. Optical microscopes are the oldest design of microscope and were possibly designed in their present compound form in the...
and the telescope
Optical telescope
An optical telescope is a telescope which is used to gather and focus light mainly from the visible part of the electromagnetic spectrum for directly viewing a magnified image for making a photograph, or collecting data through electronic image sensors....
which were both invented by the Dutch in the late 16th century.
Microscopes were first developed with just two lenses: an objective lens and an eyepiece
Eyepiece
An eyepiece, or ocular lens, is a type of lens that is attached to a variety of optical devices such as telescopes and microscopes. It is so named because it is usually the lens that is closest to the eye when someone looks through the device. The objective lens or mirror collects light and brings...
. The objective lens is essentially a magnifying glass and was designed with a very small focal length while the eyepiece generally has a longer focal length. This has the effect of producing magnified images of close objects. Generally, an additional source of illumination is used since magnified images are dimmer due to the conservation of energy
Conservation of energy
The nineteenth century law of conservation of energy is a law of physics. It states that the total amount of energy in an isolated system remains constant over time. The total energy is said to be conserved over time...
and the spreading of light rays over a larger surface area. Modern microscopes, known as compound microscopes have many lenses in them (typically four) to optimize the functionality and enhance image stability. A slightly different variety of microscope, the comparison microscope
Comparison microscope
A comparison microscope is a device used to analyze side-by-side specimens. It consists of two microscopes connected by an optical bridge, which results in a split view window enabling two separate objects to be viewed simultaneously...
, looks at side-by-side images to produce a stereoscopic binocular
Binocular vision
Binocular vision is vision in which both eyes are used together. The word binocular comes from two Latin roots, bini for double, and oculus for eye. Having two eyes confers at least four advantages over having one. First, it gives a creature a spare eye in case one is damaged. Second, it gives a...
view that appears three dimensional when used by humans.
The first telescopes, called refracting telescope
Refracting telescope
A refracting or refractor telescope is a type of optical telescope that uses a lens as its objective to form an image . The refracting telescope design was originally used in spy glasses and astronomical telescopes but is also used for long focus camera lenses...
s were also developed with a single objective and eyepiece lens. In contrast to the microscope, the objective lens of the telescope was designed with a large focal length to avoid optical aberrations. The objective focuses an image of a distant object at its focal point which is adjusted to be at the focal point of an eyepiece of a much smaller focal length. The main goal of a telescope is not necessarily magnification, but rather collection of light which is determined by the physical size of the objective lens. Thus, telescopes are normally indicated by the diameters of their objectives rather than by the magnification which can be changed by switching eyepieces. Because the magnification of a telescope is equal to the focal length of the objective divided by the focal length of the eyepiece, smaller focal-length eyepieces cause greater magnification.
Since crafting large lenses is much more difficult than crafting large mirrors, most modern telescopes are reflecting telescope
Reflecting telescope
A reflecting telescope is an optical telescope which uses a single or combination of curved mirrors that reflect light and form an image. The reflecting telescope was invented in the 17th century as an alternative to the refracting telescope which, at that time, was a design that suffered from...
s, that is, telescopes that use a primary mirror rather than an objective lens. The same general optical considerations apply to reflecting telescopes that applied to refracting telescopes, namely, the larger the primary mirror, the more light collected, and the magnification is still equal to the focal length of the primary mirror divided by the focal length of the eyepiece. Professional telescopes generally do not have eyepieces and instead place an instrument (often a charge-coupled device) at the focal point instead.
Photography
Photography
Photography is the art, science and practice of creating durable images by recording light or other electromagnetic radiation, either electronically by means of an image sensor or chemically by means of a light-sensitive material such as photographic film...
involves both lenses
Photographic lens
A camera lens is an optical lens or assembly of lenses used in conjunction with a camera body and mechanism to make images of objects either on photographic film or on other media capable of storing an image chemically or electronically.While in principle a simple convex lens will suffice, in...
and the medium in which the electromagnetic radiation is recorded, whether it be a plate, film
Photographic film
Photographic film is a sheet of plastic coated with an emulsion containing light-sensitive silver halide salts with variable crystal sizes that determine the sensitivity, contrast and resolution of the film...
, or charge-coupled device
Charge-coupled device
A charge-coupled device is a device for the movement of electrical charge, usually from within the device to an area where the charge can be manipulated, for example conversion into a digital value. This is achieved by "shifting" the signals between stages within the device one at a time...
. Photographers must consider the reciprocity
Reciprocity (photography)
In photography reciprocity refers to the inverse relationship between the intensity and duration of light that determines the reaction of light-sensitive material. Within a normal exposure range for film stock, for example, the reciprocity law states that the film response will be determined by the...
of the camera and the shot which is summarized by the relation
- Exposure ∝ ApertureArea × ExposureTime × SceneLuminance
In other words, the smaller the aperture (giving greater depth of focus), the less light coming in, so the length of time has to be increased (leading to possible blurriness if motion occurs). An example of the use of the law of reciprocity is the Sunny 16 rule
Sunny 16 rule
In photography, the Sunny 16 rule is a method of estimating correct daylight exposures without a light meter. Apart from the obvious advantage of independence from a light meter, the Sunny 16 rule can also aid in achieving correct exposure of difficult subjects...
which gives a rough estimate for the settings needed to estimate the proper exposure
Exposure (photography)
In photography, exposure is the total amount of light allowed to fall on the photographic medium during the process of taking a photograph. Exposure is measured in lux seconds, and can be computed from exposure value and scene luminance over a specified area.In photographic jargon, an exposure...
in daylight.
A camera's aperture is measured by a unitless number called the f-number
F-number
In optics, the f-number of an optical system expresses the diameter of the entrance pupil in terms of the focal length of the lens; in simpler terms, the f-number is the focal length divided by the "effective" aperture diameter...
or f-stop, #, often notated as
, and given bywhere
is the focal lengthFocal length
The focal length of an optical system is a measure of how strongly the system converges or diverges light. For an optical system in air, it is the distance over which initially collimated rays are brought to a focus...
, and
is the diameter of the entrance pupil. By convention, "#" is treated as a single symbol, and specific values of # are written by replacing the number signNumber sign
Number sign is a name for the symbol #, which is used for a variety of purposes including, in some countries, the designation of a number...
with the value. The two ways to increase the f-stop are to either decrease the diameter of the entrance pupil or change to a longer focal length (in the case of a zoom lens
Zoom lens
A zoom lens is a mechanical assembly of lens elements for which the focal length can be varied, as opposed to a fixed focal length lens...
, this can be done by simply adjusting the lens). Higher f-numbers also have a larger depth of field
Depth of field
In optics, particularly as it relates to film and photography, depth of field is the distance between the nearest and farthest objects in a scene that appear acceptably sharp in an image...
due to the lens approaching the limit of a pinhole camera
Pinhole camera
A pinhole camera is a simple camera without a lens and with a single small aperture – effectively a light-proof box with a small hole in one side. Light from a scene passes through this single point and projects an inverted image on the opposite side of the box...
which is able to focus all images perfectly, regardless of distance, but requires very long exposure times.
The field of view that the lens will provide changes with the focal length of the lens. There are three basic classifications based on the relationship to the diagonal size of the film or sensor size of the camera to the focal length of the lens:
- Normal lensNormal lensIn photography and cinematography a normal lens, also called a standard lens, is a lens that reproduces perspective that generally looks "natural" to a human observer under normal viewing conditions, as compared with lenses with longer or shorter focal lengths which produce an expanded or...
: angle of view of about 50° (called normal because this angle considered roughly equivalent to human vision) and a focal length approximately equal to the diagonal of the film or sensor. - Wide-angle lensWide-angle lensFrom a design perspective, a wide angle lens is one that projects a substantially larger image circle than would be typical for a standard design lens of the same focal length; this enables either large tilt & shift movements with a view camera, or lenses with wide fields of view.More informally,...
: angle of view wider than 60° and focal length shorter than a normal lens. - Long focus lens: angle of view narrow than a normal lens. This is any lens with a focal length longer than the diagonal measure of the film or sensor. The most common type of long focus lens is the telephoto lensTelephoto lensIn photography and cinematography, a telephoto lens is a specific type of a long-focus lens in which the physical length of the lens is shorter than the focal length. This is achieved by incorporating a special lens group known as a telephoto group that extends the light path to create a long-focus...
, a design that uses a special telephoto group to be physically shorter than its focal length.
Modern zoom lens
Zoom lens
A zoom lens is a mechanical assembly of lens elements for which the focal length can be varied, as opposed to a fixed focal length lens...
es may have some or all of these attributes.
The absolute value for the exposure time required depends on how sensitive
Sensitometry
Sensitometry is the scientific study of light-sensitive materials, especially photographic film. The study has its origins in the work by Ferdinand Hurter and Vero Charles Driffield with early black-and-white emulsions...
to light the medium being used is (measured by the film speed
Film speed
Film speed is the measure of a photographic film's sensitivity to light, determined by sensitometry and measured on various numerical scales, the most recent being the ISO system....
, or, for digital media, by the quantum efficiency
Quantum efficiency
Quantum efficiency is a quantity defined for a photosensitive device such as photographic film or a charge-coupled device as the percentage of photons hitting the photoreactive surface that will produce an electron–hole pair. It is an accurate measurement of the device's electrical sensitivity to...
). Early photography used media that had very low light sensitivity, and so exposure times had to be long even for very bright shots. As technology has improved, so has the sensitivity through film cameras and digital cameras.
Other results from physical and geometrical optics apply to camera optics. For example, the maximum resolution capability of a particular camera set-up is determined by the diffraction limit associated with the pupil size and given, roughly, by the Rayleigh criterion.
Atmospheric optics
Rayleigh scattering
Rayleigh scattering, named after the British physicist Lord Rayleigh, is the elastic scattering of light or other electromagnetic radiation by particles much smaller than the wavelength of the light. The particles may be individual atoms or molecules. It can occur when light travels through...
which redirects higher frequency (blue) sunlight back into the field of view of the observer. Because blue light is scattered more easily than red light, the sun takes on a reddish hue when it is observed through a thick atmosphere, as during a sunrise
Sunrise
Sunrise is the instant at which the upper edge of the Sun appears above the horizon in the east. Sunrise should not be confused with dawn, which is the point at which the sky begins to lighten, some time before the sun itself appears, ending twilight...
or sunset
Sunset
Sunset or sundown is the daily disappearance of the Sun below the horizon in the west as a result of Earth's rotation.The time of sunset is defined in astronomy as the moment the trailing edge of the Sun's disk disappears below the horizon in the west...
. Additional particulate matter in the sky can scatter different colors at different angles creating colorful glowing skies at dusk and dawn. Scattering off of ice crystals and other particles in the atmosphere are responsible for halos
Halo (optical phenomenon)
A halo from Greek ἅλως; also known as a nimbus, icebow or gloriole) is an optical phenomenon produced by ice crystals creating colored or white arcs and spots in the sky. Many are near the sun or moon but others are elsewhere and even in the opposite part of the sky...
, afterglow
Afterglow
An afterglow is a broad high arch of whitish or rosy light appearing in the sky due to very fine particles of dust suspended in the high regions of the atmosphere. An afterglow may appear above the highest clouds in the hour of deepening twilight, or reflected from the high snowfields in mountain...
s, coronas
Corona (meteorology)
In meteorology, a corona is produced by the diffraction of light from either the Sun or the Moon by individual small water droplets of a cloud....
, rays of sunlight
Crepuscular rays
Crepuscular rays , in atmospheric optics, are rays of sunlight that appear to radiate from a single point in the sky. These rays, which stream through gaps in clouds or between other objects, are columns of sunlit air separated by darker cloud-shadowed regions...
, and sun dog
Sun dog
A sun dog or sundog, scientific name parhelion ; , also called a mock sun or a phantom sun, is an atmospheric phenomenon that creates bright spots of light in the sky, often on a luminous ring or halo on either side of the sun.Sundogs may appear as a colored patch of light to the left or right of...
s. The variation in these kinds of phenomena is due to different particle sizes and geometries.
Mirage
Mirage
A mirage is a naturally occurring optical phenomenon in which light rays are bent to produce a displaced image of distant objects or the sky. The word comes to English via the French mirage, from the Latin mirare, meaning "to look at, to wonder at"...
s are optical phenomena in which light rays are bent due to thermal variations in the refraction index of air, producing displaced or heavily distorted images of distant objects. Other dramatic optical phenomena associated with this include the Novaya Zemlya effect
Novaya Zemlya effect
The Novaya Zemlya effect is a polar mirage caused by high refraction of sunlight between atmospheric thermoclines. The Novaya Zemlya effect will give the impression that the sun is rising earlier than it actually should and depending on the meteorological situation the effect will present the sun...
where the sun appears to rise earlier than predicted with a distorted shape. A spectacular form of refraction occurs with a temperature inversion
Inversion (meteorology)
In meteorology, an inversion is a deviation from the normal change of an atmospheric property with altitude. It almost always refers to a temperature inversion, i.e...
called the Fata Morgana
Fata Morgana (mirage)
A Fata Morgana is an unusual and very complex form of mirage, a form of superior mirage, which, like many other kinds of superior mirages, is seen in a narrow band right above the horizon...
where objects on the horizon or even beyond the horizon, such as islands, cliffs, ships or icebergs, appear elongated and elevated, like "fairy tale castles".
Rainbow
Rainbow
A rainbow is an optical and meteorological phenomenon that causes a spectrum of light to appear in the sky when the Sun shines on to droplets of moisture in the Earth's atmosphere. It takes the form of a multicoloured arc...
s are the result of a combination of internal reflection and dispersive refraction of light in raindrops. A single reflection off the backs of an array of raindrops produces a rainbow with an angular size on the sky that ranges from 40° to 42° with red on the outside. Double rainbows are produced by two internal reflections with angular size of 50.5° to 54° with violet on the outside. Because rainbows are seen with the sun 180° away from the center of the rainbow, rainbows are more prominent the closer the sun is to the horizon.
See also
- Important publications in optics
- List of optical topics
External links
Relevant discussionsTextbooks and tutorials
- Optics – an open-source optics textbook
- Optics2001 – Optics library and community
- Fundamental Optics – CVI Melles Griot Technical Guide
- Physics of Light and Optics – Brigham Young University Undergraduate Book
Wikibooks modules
- Physics Study Guide/Optics
- Optics
Further reading
Societies
- SPIE – link
- Optical Society of AmericaOptical Society of AmericaThe Optical Society is a scientific society dedicated to advancing the study of light—optics and photonics—in theory and application, by means of publishing, organizing conferences and exhibitions, partnership with industry, and education. The organization has members in more than 100 countries...
– link - European Optical SocietyEuropean Optical Society- History :*Until 1984: Optics in Europe is represented by the European Optical Committee .*1984: The EOC joins the European Physical Society to create an Optics Division....
– link
- European Photonics Industry ConsortiumEuropean Photonics Industry ConsortiumThe European Photonics Industry Consortium is a not-for-profit association with headquarters in Paris, France. EPIC serves the photonics community through a regular series of workshops, market studies and partnering...
– link - Optical Society of India – link
- Dutch Photonics Society – link