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Focal length
From Wikipedia, the free encyclopedia
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.
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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.
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:
- 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.
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.
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:
![\frac{1}{f} = (n-1) \left[ \frac{1}{R_1} - \frac{1}{R_2} + \frac{(n-1)d}{n R_1 R_2} \right],](http://upload.wikimedia.org/math/d/5/d/d5d9b5b95cf3fd9ea7f2549ae4ee8fa6.png)
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 corresponding front focal distance is:
and the back focal distance:
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.
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.
The nominal focal length of a photographic lens is the lens' 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. Some cameras have fixed focus lenses which cannot be adjusted.
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.
- 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.
- Understanding Camera Lenses - focal length & f-number - includes interactive images clarifying its influence on perspective, a required focal length calculator, and discussion of zoom vs. prime lenses