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

For a thick lens (one which has a non-negligible thickness), or an imaging system consisting of several lenses (e.g., a photographic lens), the focal length is often called the effective focal length (EFL), to distinguish it from four other commonly-used parameters:

• Front focal length is the distance from the front principal plane to the front focal point. In air, this is equal to the EFL.
• Rear focal length is the distance from the rear principal plane to the rear focal point. In air, this is also equal to the EFL.
• Front focal distance (FFD) is the distance from the front focal point of the system to the first optical surface.
• Back focal distance (BFD) is the distance from the last optical surface of the system to the rear focal point.

The front/rear focal lengths and focal distances are often confused, and the notations FFL and BFL/RFL can refer to either.

Symmetric single-lens optical systems will have identical values for their front and rear focal lengths and distances. For a thin lens (one which has a negligible thickness), all of the focal lengths and distances are equal and are measured from the same point: the middle of the lens.

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:

${\displaystyle {\frac {1}{f}}=(n-1)\left,}$

where n is the refractive index of the lens medium.

The corresponding front focal distance is:

${\displaystyle {\mbox{FFD}}=f\left(1+{\frac {(n-1)d}{nR_{2}}}\right),}$

and the back focal distance:

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

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.

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

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

References

• Grievenkamp, John E. (2004). Field Guide to Geometrical Optics. SPIE Field Guides vol. FG01. SPIE. ISBN 0819452947.
• Hecht, Eugene (2001). Optics (4th ed. ed.). Pearson Education. ISBN 0805385665. {{cite book}}: |edition= has extra text (help)

• Optics
• Photographic terms
• Length