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The focal length of a lens is the distance along the optical axis from the lens to the principal focus (or focal point). The inverse of a lens' focal length is called its power.

For a converging lens (e.g., a convex lens), the focal length is positive, and is the distance from the lens 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 from the lens to the point at which a collimated beam appears to be emerging from 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), three focal lengths can be defined:

• The effective focal length (EFL), or the distance from the principal point to the focal point.
• The front focal length (FFL), or the distance from the first (front) focal point of the system to the first optical surface.
• The back focal length (BFL), or the distance from the second (back) focal point to the last optical surface of the system.

In general, the EFL is used to describe the focal length of a lens or optical system, and is the value used to calculate the magnification of the system.

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

For the case of a lens of thickness d, 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 length is:

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

and the back focal length:

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

In the standard sign convention, the value of R₁ will be positive if the first lens surface if convex, and negative if concave. The value of R₂ is negative if the second surface is concave, positive if convex.

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

• Normal lens
• Telephoto lens
• Wide-angle lens
• Depth-of-field

• Optics
• Photographic terms
• Length