Focus (optics)

Eye focusing ideally collects all light rays from a point on an object into a corresponding point on the retina.
A demonstration of camera focus on different distances, showing a bamboo rooftop
Text on a page that is partially in focus, but mostly not in varying degrees

Image point, is a point where light rays originating from a point on the object converge.

- Focus (optics)

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Cassegrain reflector

Combination of a primary concave mirror and a secondary convex mirror, often used in optical telescopes and radio antennas, the main characteristic being that the optical path folds back onto itself, relative to the optical system's primary mirror entrance aperture.

Light path in a Cassegrain reflecting telescope
Light path in a Cassegrain reflector telescope
A Cassegrain radio antenna at GDSCC

This design puts the focal point at a convenient location behind the primary mirror and the convex secondary adds a telephoto effect creating a much longer focal length in a mechanically short system.

Airy disk

A computer-generated image of an Airy disk. The grayscale intensities have been adjusted to enhance the brightness of the outer rings of the Airy pattern.
A computer-generated Airy disk from diffracted white light (D65 spectrum). Note that the red component is diffracted more than the blue, so that the center appears slightly bluish.
A real Airy disk created by passing a red laser beam through a 90-micrometre pinhole aperture with 27 orders of diffraction
Airy disk captured by 2000 mm camera lens at f/25 aperture. Image size: 1×1 mm.
Log-log plot of aperture diameter vs angular resolution at the diffraction limit for various light wavelengths compared with various astronomical instruments. For example, the blue star shows that the Hubble Space Telescope is almost diffraction-limited in the visible spectrum at 0.1 arcsecs, whereas the red circle shows that the human eye should have a resolving power of 20 arcsecs in theory, though 20/20 vision resolves to only 60 arcsecs (1 arcminute)
Longitudinal sections through a focused beam with (top) negative, (center) zero, and (bottom) positive spherical aberration. The lens is to the left.

In optics, the Airy disk (or Airy disc) 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.

Cardinal point (optics)

In Gaussian optics, the cardinal points consist of three pairs of points located on the optical axis of a rotationally symmetric, focal, optical system.

The cardinal points of a thick lens in air. F, F' front and rear focal points, P, P' front and rear principal points, V, V' front and rear surface vertices.
Rays that leave the object with the same angle cross at the back focal plane.
Angle filtering with an aperture at the rear focal plane.
Various lens shapes, and the location of the principal planes. (There is an error in the 8th figure: r1 should be +.)
N, N' The front and rear nodal points of a thick lens.

These are the focal points, the principal points, and the nodal points.

Curved mirror

Mirror with a curved reflecting surface.

Reflections in a convex mirror. The photographer is seen reflected at top right
A convex mirror diagram showing the focus, focal length, centre of curvature, principal axis, etc.
Convex mirror lets motorists see around a corner.
Detail of the convex mirror in the Arnolfini Portrait
A virtual image in a Christmas bauble.
A concave mirror diagram showing the focus, focal length, centre of curvature, principal axis, etc.

Such mirrors always form a virtual image, since the focal point (F) and the centre of curvature (2F) are both imaginary points "inside" the mirror, that cannot be reached.

Focal length

Optical system is a measure of how strongly the system converges or diverges light; it is the inverse of the system's optical power.

The focal point F and focal length f of a positive (convex) lens, a negative (concave) lens, a concave mirror, and a convex mirror.
Thick lens diagram
Images of black letters in a thin convex lens of focal length f are shown in red. Selected rays are shown for letters E, I and K in blue, green and orange, respectively. Note that E (at 2f) has an equal-size, real and inverted image; I (at f) has its image at infinity; and K (at f⁄2) has a double-size, virtual and upright image.
In this computer simulation, adjusting the field of view (by changing the focal length) while keeping the subject in frame (by changing accordingly the position of the camera) results in vastly differing images. At focal lengths approaching infinity (0 degrees of field of view), the light rays are nearly parallel to each other, resulting in the subject looking "flattened". At small focal lengths (bigger field of view), the subject appears "foreshortened".

For the special case of a thin lens in air, a positive focal length is the distance over which initially collimated (parallel) rays are brought to a focus, or alternatively a negative focal length indicates how far in front of the lens a point source must be located to form a collimated beam.

Defocus aberration

A photograph of Christmas lights with significant defocus aberration.

In optics, defocus is the aberration in which an image is simply out of focus.

Circle of confusion

Diagram showing circles of confusion for point source too close, in focus, and too far
An early calculation of CoC diameter ("indistinctness") by "T.H." in 1866.

In optics, a circle of confusion (CoC) 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.

Geometrical optics

Model of optics that describes light propagation in terms of rays.

As light travels through space, it oscillates in amplitude. In this image, each maximum amplitude crest is marked with a plane to illustrate the wavefront. The ray is the arrow perpendicular to these parallel surfaces.
Diagram of specular reflection
Illustration of Snell's Law

For mirrors with parabolic surfaces, parallel rays incident on the mirror produce reflected rays that converge at a common focus.

Lens

Transmissive optical device which focuses or disperses a light beam by means of refraction.

A biconvex lens
Lenses can be used to focus light
Light being refracted by a spherical glass container full of water. Roger Bacon, 13th century
Lens for LSST, a planned sky surveying telescope
Types of lenses
The position of the focus of a spherical lens depends on the radii of curvature of the two facets.
A camera lens forms a real image of a distant object.
Virtual image formation using a positive lens as a magnifying glass.
Images of black letters in a thin convex lens of focal length f are shown in red. Selected rays are shown for letters E, I and K in blue, green and orange, respectively. Note that E (at 2f) has an equal-size, real and inverted image; I (at f) has its image at infinity; and K (at f/2) has a double-size, virtual and upright image.
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An aspheric biconvex lens.
Close-up view of a flat Fresnel lens.

As mentioned above, a positive or converging lens in air focuses a collimated beam travelling along the lens axis to a spot (known as the focal point) at a distance f from the lens.

Aperture

Aperture is a hole or an opening through which light travels.

Different apertures of a lens
Definitions of Aperture in the 1707 Glossographia Anglicana Nova
Alvin Clark polishes the big Yerkes Observatory Great Refractor objective lens, with 40 inches 102 cm across, in 1896.
Diagram of decreasing aperture sizes (increasing f-numbers) for "full stop" increments (factor of two aperture area per stop)
The aperture range of a 50mm Minolta lens, f/1.4–f/16
Aperture mechanism of Canon 50mm f/1.8 II lens, with five blades
{{f/|32}} – small aperture and slow shutter
{{f/|5.6}} – large aperture and fast shutter
{{f/|22}} – small aperture and slower shutter (Exposure time: 1/80)
{{f/|3.5}} – large aperture and faster shutter (Exposure time: 1/2500)
Changing a camera's aperture value in half-stops, beginning with {{f/|256}} and ending with {{f/|1}}
Changing a camera's aperture diameter from zero to infinity

More specifically, the aperture and focal length of an optical system determine the cone angle of a bundle of rays that come to a focus in the image plane.