In 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...

, 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

Circle of confusion

In optics, a circle of confusion is an optical spot caused by a cone of light rays from a lens not coming to a perfect focus when imaging a point source...

. This non-ideal focusing may be caused by aberrations of the imaging optics. In the absence of significant aberrations, the smallest possible blur circle is the Airy disc

Airy disc

In optics, the Airy disk and Airy pattern are descriptions of the best focused spot of light that a perfect lens with a circular aperture can make, limited by the diffraction of light....

, which is caused by 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...

 from the optical system's 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,...

. Aberrations tend to get worse as the aperture diameter increases, while the Airy circle is smallest for large apertures.

An image, or image point or region, is in focus if light from object points is converged almost as much as possible in the image, and out of focus if light is not well converged. The border between these is sometimes defined using a circle of confusion

Circle of confusion

In optics, a circle of confusion is an optical spot caused by a cone of light rays from a lens not coming to a perfect focus when imaging a point source...

 criterion.

A principal focus or focal point is a special focus:

• For a 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...
  
  , or a spherical
  Sphere
  A sphere is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball. Like a circle in two dimensions, a perfect sphere is completely symmetrical around its center, with all points on the surface lying the same distance r from the center point...
  
   or parabolic
  Parabola
  In mathematics, the parabola is a conic section, the intersection of a right circular conical surface and a plane parallel to a generating straight line of that surface...
  
   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...
  
  , it is a point onto which collimated light
  Collimated light
  Collimated light is light whose rays are parallel, and therefore will spread slowly as it propagates. The word is related to "collinear" and implies light that does not disperse with distance , or that will disperse minimally...
  
   parallel to the axis is focused. Since light can pass through a lens in either direction, a lens has two focal points—one on each side. The distance in air from the lens or mirror's principal plane to the focus is called the focal length
  Focal 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...
  
  .
• Elliptical
  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...
  
   mirrors have two focal points: light that passes through one of these before striking the mirror is reflected such that it passes through the other.
• The focus of a hyperbolic
  Hyperbola
  In mathematics a hyperbola is a curve, specifically a smooth curve that lies in a plane, which can be defined either by its geometric properties or by the kinds of equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, which are mirror...
  
   mirror is either of two points which have the property that light from one is reflected as if it came from the other.

A diverging (negative) lens, or a convex mirror, does not focus a collimated beam to a point. Instead, the focus is the point from which the light appears to be emanating, after it travels through the lens or reflects from the mirror. A convex parabolic mirror will reflect a beam of collimated light to make it appear as if it were radiating from the focal point, or conversely, reflect rays directed toward the focus

Focus (geometry)

In geometry, the foci are a pair of special points with reference to which any of a variety of curves is constructed. For example, foci can be used in defining conic sections, the four types of which are the circle, ellipse, parabola, and hyperbola...

 as a collimated beam. A convex elliptical mirror will reflect light directed towards one focus as if it were radiating from the other focus, both of which are behind the mirror. A convex hyperbolic

Hyperbola

In mathematics a hyperbola is a curve, specifically a smooth curve that lies in a plane, which can be defined either by its geometric properties or by the kinds of equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, which are mirror...

 mirror will reflect rays emanating from the focal point

Focus (geometry)

In geometry, the foci are a pair of special points with reference to which any of a variety of curves is constructed. For example, foci can be used in defining conic sections, the four types of which are the circle, ellipse, parabola, and hyperbola...

 in front of the mirror as if they were emanating from the focal point behind the mirror. Conversely, it can focus rays directed at the focal point that is behind the mirror towards the focal point that is in front of the mirror as in a Cassegrain telescope

Cassegrain reflector

The Cassegrain reflector is a combination of a primary concave mirror and a secondary convex mirror, often used in optical telescopes and radio antennas....

.

See also

• Autofocus
  Autofocus
  An autofocus optical system uses a sensor, a control system and a motor to focus fully automatic or on a manually selected point or area. An electronic rangefinder has a display instead of the motor; the adjustment of the optical system has to be done manually until indication...
  
  
• Cardinal point (optics)
  Cardinal point (optics)
  In Gaussian optics, the cardinal points consist of three pairs of points located on the optical axis of an ideal, rotationally symmetric, focal, optical system...
  
  
• Defocus aberration
  Defocus aberration
  In optics, defocus is the aberration in which an image is simply out of focus. This aberration is familiar to anyone who has used a camera, videocamera, microscope, telescope, or binoculars. Optically, defocus refers to a translation along the optical axis away from the plane or surface of best...
  
  
• 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...
  
  
• Depth of focus
  Depth of focus
  Depth of focus is a lens optics concept that measures the tolerance of placement of the image plane in relation to the lens...
  
  
• 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...
  
  
• Focus (geometry)
  Focus (geometry)
  In geometry, the foci are a pair of special points with reference to which any of a variety of curves is constructed. For example, foci can be used in defining conic sections, the four types of which are the circle, ellipse, parabola, and hyperbola...
  
  
• Fixed focus
• Bokeh
  Bokeh
  In photography, bokeh is the blur, or the aesthetic quality of the blur, in out-of-focus areas of an image, or "the way the lens renders out-of-focus points of light."...
  
  
• Focus stacking
  Focus stacking
  Focus stacking is a digital image processing technique which combines multiple images taken at different focus distances to give a resulting image with a greater depth of field than any of the individual source images...