Rayleigh scattering
Encyclopedia
Elastic scattering
In scattering theory and in particular in particle physics, elastic scattering is one of the specific forms of scattering. In this process, the kinetic energy of the incident particles is conserved, only their direction of propagation is modified .-Electron elastic scattering:When an alpha particle...
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...
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...
or other electromagnetic
Electromagnetism
Electromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...
radiation by particles much smaller than 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. The particles may be individual atoms or molecules. It can occur when light travels through transparent solids and liquids, but is most prominently seen in gas
Gas
Gas is one of the three classical states of matter . Near absolute zero, a substance exists as a solid. As heat is added to this substance it melts into a liquid at its melting point , boils into a gas at its boiling point, and if heated high enough would enter a plasma state in which the electrons...
es. Rayleigh scattering is a function of the electric polarizability
Polarizability
Polarizability is the measure of the change in a molecule's electron distribution in response to an applied electric field, which can also be induced by electric interactions with solvents or ionic reagents. It is a property of matter...
of the particles.
Rayleigh scattering of sunlight
Sunlight
Sunlight, in the broad sense, is the total frequency spectrum of electromagnetic radiation given off by the Sun. On Earth, sunlight is filtered through the Earth's atmosphere, and solar radiation is obvious as daylight when the Sun is above the horizon.When the direct solar radiation is not blocked...
in the atmosphere causes diffuse sky radiation
Diffuse sky radiation
Diffuse sky radiation is solar radiation reaching the Earth's surface after having been scattered from the direct solar beam by molecules or suspensoids in the atmosphere. It is also called skylight, diffuse skylight, or sky radiation and is the reason for changes in the colour of the sky...
, which is the reason for the blue color of the sky and the yellow tone of the sun itself.
Scattering by particles similar to or larger than the wavelength of light is typically treated by the Mie theory
Mie theory
The Mie solution to Maxwell's equations describes the scattering of electromagnetic radiation by a sphere...
, the discrete dipole approximation
Discrete dipole approximation
The discrete dipole approximation is a method for computing scattering of radiation by particles of arbitrary shape and by periodic structures. Given a target of arbitrary geometry, one seeks to calculate its scattering and absorption properties...
and other computational techniques. Rayleigh scattering applies to particles that are small with respect to wavelengths of light, and that are optically "soft" (i.e. with a refractive index close to 1). On the other hand, Anomalous Diffraction Theory
Anomalous Diffraction Theory
Anomalous Diffraction Theory - approximation developed by van de Hulst describing light scattering for optically soft spheres....
applies to optically soft but larger particles.
Small size parameter approximation
The size of a scattering particle is parameterized by the ratio x of its characteristic dimension r and wavelengthWavelength
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...
λ:
Rayleigh scattering can be defined as scattering in the small size parameter regime . Scattering from larger spherical particles is explained by the Mie theory
Mie theory
The Mie solution to Maxwell's equations describes the scattering of electromagnetic radiation by a sphere...
for an arbitrary size parameter x. For small x the Mie theory reduces to the Rayleigh approximation.
The amount of Rayleigh scattering that occurs for a beam of light depends upon the size of the particles and the wavelength of the light. Specifically, the intensity of the scattered light varies as the sixth power of the particle size, and varies inversely with the fourth power of the wavelength .
The intensity
Intensity (physics)
In physics, intensity is a measure of the energy flux, averaged over the period of the wave. The word "intensity" here is not synonymous with "strength", "amplitude", or "level", as it sometimes is in colloquial speech...
I of light scattered by a single small particle from a beam of unpolarized light of wavelength λ and intensity I0 is given by:
where R is the distance to the particle, θ is the scattering angle, n is 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....
of the particle, and d is the diameter of the particle.
The Rayleigh scattering coefficient for a group of scattering particles is the number of particles per unit volume N times the cross-section. As with all 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, for incoherent
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....
scattering the scattered powers add arithmetically, while for coherent scattering, such as if the particles are very near each other, the fields add arithmetically and the sum must be squared to obtain the total scattered power.
Rayleigh scattering from molecules
.jpg)
Polarizability
Polarizability is the measure of the change in a molecule's electron distribution in response to an applied electric field, which can also be induced by electric interactions with solvents or ionic reagents. It is a property of matter...
α, which describes how much the electrical charges on the molecule will move in an electric field. In this case, the Rayleigh scattering intensity for a single particle is given by
The amount of Rayleigh scattering from a single particle can also be expressed as a cross section
Absorption cross section
Absorption cross section is a measure for the probability of an absorption process. More generally, the term cross section is used in physics to quantify the probability of a certain particle-particle interaction, e.g., scattering, electromagnetic absorption, etc...
σ. For example, the major constituent of the atmosphere, nitrogen, has a Rayleigh cross section of at a wavelength of 532 nm (green light). This means that at atmospheric
pressure, about a fraction 10−5 of light will be scattered for every meter of travel.
The strong wavelength dependence of the scattering (~λ−4) means that shorter (blue
Blue
Blue is a colour, the perception of which is evoked by light having a spectrum dominated by energy with a wavelength of roughly 440–490 nm. It is considered one of the additive primary colours. On the HSV Colour Wheel, the complement of blue is yellow; that is, a colour corresponding to an equal...
) wavelengths are scattered more strongly than longer (red
Red
Red is any of a number of similar colors evoked by light consisting predominantly of the longest wavelengths of light discernible by the human eye, in the wavelength range of roughly 630–740 nm. Longer wavelengths than this are called infrared , and cannot be seen by the naked eye...
) wavelengths. This results in the indirect blue light coming from all regions of the sky. Rayleigh scattering is a good approximation of the manner in which light scattering occurs within various media for which scattering particles have a small size parameter.
Reason for the blue color of the sky
A portion of the light coming from the sun scatters off molecules and other small particles in the atmosphere. It is this scattered light that gives the sky its brightness and its color. As previously explained, Rayleigh scattering is inversely proportional to the fourth power of wavelength, so that shorter wavelength violet and blue light will scatter more than the longer wavelengths (yellow and especially red light). The resulting color, which appears like a pale blue, actually is a "weighted average" of all the scattered colors, mainly blue and green. Violet, though strongly scattered, is a minor component of the solar spectrum and is less efficiently detected by the human eye; its hueHue
Hue is one of the main properties of a color, defined technically , as "the degree to which a stimulus can be describedas similar to or different from stimuli that are described as red, green, blue, and yellow,"...
is intermediate between blue and green. Conversely, glancing toward the sun, the colors that were not scattered away—-the longer wavelengths such as red and yellow light—-are directly visible, giving the sun itself a slightly yellowish hue. Viewed from outer space, however, the sky is black and the sun is white.
The reddening of sunlight is intensified when the sun is near the horizon, because the volume of air through which sunlight must pass is significantly greater than when the sun is high in the sky. The Rayleigh scattering effect is therefore increased, removing virtually all blue light from the direct path to the observer. The remaining unscattered light is mostly of a longer wavelength, and therefore appears to be orange.
Rayleigh scattering primarily occurs through light's interaction with air molecules. Or, from a purely "optical", macroscopic point of view, blue sky comes from microscopic density fluctuations, resulting from the random motion of molecules composing the air. A region of higher or lower density has a slightly different 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....
than the surrounding medium, and therefore it acts like a short-lived particle that can scatter light in random directions. Smaller regions fluctuate more than larger ones, and, since short wavelengths are "disturbed" by small regions more than longer wavelengths, they are scattered more.
Some of the scattering can also be from sulfate particles. For years after large Plinian eruption
Plinian eruption
Plinian eruptions, also known as 'Vesuvian eruptions', are volcanic eruptions marked by their similarity to the eruption of Mount Vesuvius in AD 79 ....
s, the blue cast of the sky is notably brightened due to the persistent sulfate load of the stratospheric
Stratospheric
Stratospheric is an instrumental guitar album , released by French guitarist Jean-Pierre Danel in 2000.Several songs from the album hit the web downloading charts, including three #1's....
gases.
In locations with little light pollution
Light pollution
Light pollution, also known as photopollution or luminous pollution, is excessive or obtrusive artificial light.The International Dark-Sky Association defines light pollution as:...
, the moonlit night sky is also blue, because moonlight is reflected sunlight, with a slightly lower color temperature
Color temperature
Color temperature is a characteristic of visible light that has important applications in lighting, photography, videography, publishing, manufacturing, astrophysics, and other fields. The color temperature of a light source is the temperature of an ideal black-body radiator that radiates light of...
due to the brownish color of the moon. The moonlit sky is not perceived as blue, however, because at low light levels human vision comes mainly from rod cells that do not produce any color perception.
Rayleigh scattering in optical fibers
Rayleigh scattering is an important component of the scattering of optical signals in optical fibers. Silica fibers are disordered materials, thus their density varies, on a microscopic scale. The density fluctuations give rise to energy loss due to the scattered light, with the following coefficient:
where n is the refraction index,
is the photoelastic coefficient of the glass, 
is Boltzmann constant, and 
is the isothermal compressibility. Tf is a fictive temperature, representing the temperature at which the density fluctuations are "frozen" in the material.Rayleigh scattering in porous materials
λ−4 Rayleigh-type scattering can also be exhibited by porous materials. An example is the strong optical scattering by nanoporous materials. The strong contrast in refractive index between pores and solid parts of sintered alumina results in very strong scattering, with light completely changing direction each 5 micrometers on average. The λ−4-type scattering is caused by the nanoporous structure (a narrow pore size distribution around ~70 nm) obtained by sinteringSintering
Sintering is a method used to create objects from powders. It is based on atomic diffusion. Diffusion occurs in any material above absolute zero, but it occurs much faster at higher temperatures. In most sintering processes, the powdered material is held in a mold and then heated to a temperature...
monodispersive alumina powder.
See also
- Rayleigh Sky ModelRayleigh sky modelThe Rayleigh sky model describes the observed polarization pattern of the daytime sky. Within the atmosphere Rayleigh scattering of light from air molecules, water, dust, and aerosols causes the sky's light to have a defined polarization pattern. The same elastic scattering processes cause the sky...
- Rayleigh fadingRayleigh fadingRayleigh fading is a statistical model for the effect of a propagation environment on a radio signal, such as that used by wireless devices.Rayleigh fading models assume that the magnitude of a signal that has passed through such a transmission medium will vary randomly, or fade, according to a...
- Ricean fading
- Raman scatteringRaman scatteringRaman 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....
- Optical phenomenonOptical phenomenonAn optical phenomenon is any observable event that results from the interaction of light and matter. See also list of optical topics and optics. A mirage is an example of an optical phenomenon....
- Dynamic light scatteringDynamic light scatteringthumb|right|350px|Hypothetical Dynamic light scattering of two samples: Larger particles on the top and smaller particle on the bottomDynamic light scattering is a technique in physics that can be used to determine the size distribution profile of small particles in suspension or polymers...
- Tyndall effectTyndall effectThe 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...
- Critical opalescenceCritical opalescenceCritical opalescence is a phenomenon which arises in the region of a continuous, or second-order, phase transition. Originally reported by Thomas Andrews in 1869 for the liquid-gas transition in carbon dioxide, many other examples have been discovered since. The phenomenon is most commonly...
- Marian SmoluchowskiMarian SmoluchowskiMarian Smoluchowski was an ethnic Polish scientist in the Austro-Hungarian Empire. He was a pioneer of statistical physics and an avid mountaineer.-Life:...
- Rayleigh Criterion
- Aerial perspectiveAerial perspectiveAerial perspective or atmospheric perspective refers to the effect the atmosphere has on the appearance of an object as it is viewed from a distance. As the distance between an object and a viewer increases, the contrast between the object and its background decreases, and the contrast of any...
Further reading
- Pedro Lilienfeld, "A Blue Sky History." (2004). Optics and Photonics News. Vol. 15, Issue 6, pp. 32–39. . Gives a brief history of theories of why the sky is blue leading up to Rayleigh's discovery, and a brief description of Rayleigh scattering.