Focal length

The focal length f of a lens or curved mirror is the distance from the optical element to the point at which parallel rays incoming along the optical axis converge (for a converging lens/mirror) or appear to diverge from (for a diverging lens/mirror, where f is taken as negative). It is the single most important parameter of an imaging system, setting the magnification at a given object distance, the angle of view, the depth of field, and the compression/expansion of perspective.

In photography, a 50 mm lens on a full-frame sensor gives roughly the angular field of human central vision (about 46° diagonal); a 24 mm lens is a wide angle (84°); a 200 mm lens is a telephoto (12°). The magnification of a distant object is proportional to f, while the angle of view is inversely proportional — longer focal lengths fill the frame with a smaller part of the scene. In microscope objectives and camera lenses, focal length combines with the numerical aperture NA to set the diffraction-limited resolution (λ/(2·NA), the Abbe limit) and the depth of field (∝ 1/NA²). The lensmaker's equation 1/f = (n−1)(1/R₁ − 1/R₂) computes f from the material index and the surface geometry; in thick or compound systems, f is computed by matrix optics as the element (1/f)-value of the system's ray-transfer matrix.