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Encyclopedia > Focal length
The focal point F and focal length f of a positive (convex) lens, a negative (concave) lens, a concave mirror, and a convex mirror.

The focal length of an optical system is a measure of how strongly it converges (focuses) or diverges (diffuses) light. A system with a shorter focal length has greater optical power than one with a long focal length. The pinhole camera model describes the mathematical relationship between the coordinates of a 3D point and its projection onto the image plane of an ideal pinhole camera. ... The pinhole camera model describes the mathematical relationship between the coordinates of a 3D point and its projection onto the image plane of an ideal pinhole camera. ... Image File history File links Diagram illustrating focal length, created by DrBob File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... For the book by Sir Isaac Newton, see Opticks. ... This article does not cite any references or sources. ... Optical power or dioptric power or refractive power is the degree to which a lens or mirror converges or diverges light. ...

## Contents

For a thin lens in air, the focal length is the distance from the center of the lens to the principal foci (or focal points) of the lens. For a converging lens (for example a convex lens), the focal length is positive, and is the distance at which a beam of collimated light will be focused to a single spot. For a diverging lens (for example a concave lens), the focal length is negative, and is the distance to the point from which a collimated beam appears to be diverging after passing through the lens. A lens can be considered a thin lens if d << f. ... A lens. ... An image that is partially in focus, but mostly out of focus in varying degrees. ... An image that is partially in focus, but mostly out of focus in varying degrees. ... A lens. ... Collimated light is light whose rays are parallel. ... A lens. ...

## General optical systems

For a thick lens (one which has a non-negligible thickness), or an imaging system consisting of several lenses and/or mirrors (e.g., a photographic lens or a telescope), the focal length is often called the effective focal length (EFL), to distinguish it from other commonly-used parameters: Although related to the more mathematical concepts of infinitesimal , the idea of something being negligible is particularly useful in practical disciplines like physics, chemistry, mechanical and electronic engineering, computer programming and in everyday decision-making. ... Photographic lens One of Canons most popular wide angle lenses - 17-40 f/4 L The zoom lens of the Canon Elph A photographic lens (or more correctly, objective) is an optical lens or assembly of lenses used in conjunction with a camera body and mechanism to make images... This article does not cite any references or sources. ...

• Front focal length (FFL) or Front focal distance (FFD) is the distance from the front focal point of the system to the vertex of the first optical surface.
• Back focal length (BFL) or Back focal distance (BFD) is the distance from the vertex of the last optical surface of the system to the rear focal point.

For an optical system in air, the effective focal length gives the distance from the front and rear principal planes to the corresponding focal points. If the surrounding medium is not air, then the distance is multiplied by the refractive index of the medium. Some authors call this distance the front (rear) focal length, distinguishing it from the front (rear) focal distance, defined above. The cardinal points and the associated cardinal planes are a set of special points and planes in an optical system, which help in the analysis of its paraxial properties. ... The cardinal points and the associated cardinal planes are a set of special points and planes in an optical system, which help in the analysis of its paraxial properties. ... The refractive index (or index of refraction) of a medium is a measure for how much the speed of light (or other waves such as sound waves) is reduced inside the medium. ...

In general, the focal length or EFL is the value that describes the ability of the optical system to focus light, and is the value used to calculate the magnification of the system. The other parameters are used in determining where an image will be formed for a given object position. Magnification is the process of enlarging something only in appearance, not physical size. ... It has been suggested that this article or section be merged into image (disambiguation). ...

For the case of a lens of thickness d in air, and surfaces with radii of curvature R1 and R2, the effective focal length f is given by: The term radius of curvature has specific meaning and sign convention in optical design. ...

$frac{1}{f} = (n-1) left[ frac{1}{R_1} - frac{1}{R_2} + frac{(n-1)d}{n R_1 R_2} right],$

where n is the refractive index of the lens medium. The quantity 1/f is also known as the optical power of the lens. The refractive index (or index of refraction) of a medium is a measure for how much the speed of light (or other waves such as sound waves) is reduced inside the medium. ... Optical power or dioptric power or refractive power is the degree to which a lens or mirror converges or diverges light. ...

The corresponding front focal distance is:

$mbox{FFD} = f left( 1 + frac{ (n-1) d}{n R_2} right),$

and the back focal distance:

$mbox{BFD} = f left( 1 - frac{ (n-1) d}{n R_1} right).$

In the most common sign convention, the value of R1 will be positive if the first lens surface is convex, and negative if it is concave. The value of R2 is negative if the second surface is concave, and positive if convex. Note that sign conventions vary between different authors, however. In physics, a sign convention is a choice of the signs (plus or minus) of a set of quantities, in a case where the choice of sign is arbitrary. ...

For a spherically curved mirror, the focal length is equal to half the radius of curvature of the mirror. The focal length is positive for a concave mirror, and negative for a convex mirror. A sphere is a symmetrical geometrical object. ... A mirror, reflecting a vase. ... The term radius of curvature has specific meaning and sign convention in optical design. ... Reflections in a spherical convex mirror. ... Reflections in a spherical convex mirror. ...

## In photography

The nominal focal length of a photographic lens is the lens's focal length when set to "infinity". By design, the rear principal plane of the lens is then separated from the photographic film or image sensor by the focal length. Objects far away from the camera then produce sharp images on the film or sensor. When the lens is adjusted to photograph objects closer to the camera, the actual focal length of the lens changes. Photographic lens One of Canons most popular wide angle lenses - 17-40 f/4 L The zoom lens of the Canon Elph A photographic lens (or more correctly, objective) is an optical lens or assembly of lenses used in conjunction with a camera body and mechanism to make images... The cardinal points and the associated cardinal planes are a set of special points and planes in an optical system, which help in the analysis of its paraxial properties. ... This article or section does not cite its references or sources. ... Hello--80. ...

Focal lengths are usually specified in millimetres (mm), but older lenses marked in centimetres (cm) and inches are still to be found. The angle of view depends on the ratio between the focal length and the film size. Due to the popularity of the 35 mm standard, lenses are often described in terms of their "35 mm equivalent" fields of view. This is the difference between a normal lens (e.g. 50 mm), wide-angle lens (e.g. 24 mm), and telephoto lens (e.g. 500 mm). This is particularly common with digital cameras, which generally use sensors smaller than 35 mm film, and so require correspondingly shorter focal lengths to generate equivalent images. A millimetre (American spelling: millimeter, symbol mm) is an SI unit of length that is equal to one thousandth of a metre. ... A centimetre (American spelling centimeter, symbol cm) is a unit of length that is equal to one hundredth of a metre, the current SI base unit of length. ... An inch (plural: inches; symbol or abbreviation: in or, sometimes, â€³ - a double prime) is the name of a unit of length in a number of different systems, including English units, Imperial units, and United States customary units. ... // Movie film formats Amateur formats: 8 mm Single-8 Super 8 mm Polavision 9,5 mm film 17. ... 135 Film Size, Kodak Tri-X 400 speed 135 (ISO 1007) is a film format for still photography. ... In photography and cinematography a normal lens is a lens that generates images that are generally held to have a natural perspective similar to human eyesight, compared with lenses with longer or shorter focal lengths. ... One of Canons most popular wide-angle lenses - 17-40 mm f/4 L retrofocus zoom lens. ... 500 mm telephoto lens with extension tube. ... A SiPix digital camera next to a matchbox to show scale Nikon D200 SLR with Nikon film scanner, which converts film images to digital A Hasselblad 503CW with a digital camera back A digital camera is an electronic device used to capture and store photographs digitally, instead of using photographic...

In optics, particularly film and photography, the depth of field (DOF) is the distance in front of and beyond the subject that appears to be in focus. ... A 35mm lens set to f/11, as indicated by the white dot above the f-stop scale on the aperture ring In photography the f-number (focal ratio) expresses the diameter of the diaphragm aperture in terms of the effective focal length of the lens. ... A dioptre, or diopter, is a non-SI unit of measurement of the optical power of a lens or curved mirror, which is equal to the reciprocal of the focal length measured in metres (i. ... An image that is partially in focus, but mostly out of focus in varying degrees. ...

## References

• Grievenkamp, John E. (2004). Field Guide to Geometrical Optics, SPIE Field Guides vol. FG01, SPIE. ISBN 0-8194-5294-7.
• Hecht, Eugene (2001). Optics, 4th ed., Pearson Education. ISBN 0-8053-8566-5.

Results from FactBites:

 Focal length - Wikipedia, the free encyclopedia (337 words) The focal length of a lens is the distance along the optical axis from the lens to the focus (or focal point). For a negative (diverging) lens, the focal length is negative, and is the distance in front of the lens to the point at which a collimated beam appears to be emerging from after passing through the lens. For a spherically curved mirror, the focal length is equal to half the radius of curvature of the mirror.
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