The focal length of an optical system is a measure of how strongly it focuses or diverges light. A system with a shorter focal length has greater optical power than one with a long focal length.

Thin lens approximation

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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 (e.g., 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 (e.g., 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.

General optical systems

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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:

$\backslash frac\{1\}\{f\}\; =\; (n-1)\; \backslash left\backslash frac\{1\}\{R\_1\}\; -\; \backslash frac\{1\}\{R\_2\}\; +\; \backslash frac\{(n-1)d\}\{n\; R\_1\; R\_2\}\; \backslash right,$

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 corresponding front focal distance is:

$\backslash mbox\{FFD\}\; =\; f\; \backslash left(\; 1\; +\; \backslash frac\{\; (n-1)\; d\}\{n\; R\_2\}\; \backslash right),$

and the back focal distance:

$\backslash mbox\{BFD\}\; =\; f\; \backslash left(\; 1\; -\; \backslash frac\{\; (n-1)\; d\}\{n\; R\_1\}\; \backslash right).$

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.

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.

See also

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• Depth-of-field
• Dioptre
• Focus (optics)
• Normal lens
• Telephoto lens
• Wide-angle lens

References

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External links

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• 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

Geometrical optics | Photographic terms | Length

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