Focal length, EFL, and the eye

Abstract

The focal length is often called the effective focal length, or efl instead, and although this is acceptable for a lens in air, it is not otherwise correct. The eye is used as an example here for an optical system where the object is in air and the image is in fluid. Welford, Aberrations of Optical Systems (1986) has paraxial equations that are consistent with historical use while also clearly defining efl. These are based on power at a surface having to be the same for light traveling in both directions (n ^'/f ^'). The focal length f ^' is the actual physical distance from the 2nd principal point to the paraxial focus, and the equivalent focal length, or efl, is the focal length divided by the image index (f ^'/n ^'). Separately, when the object is in air, the efl is shown to act at the nodal point, with the lens system represented by either an equivalent thin lens at the principal point with a focal length or a different equivalent thin lens in air at the nodal point with an efl. The rationale for using effective instead of equivalent for efl is unclear, but efl is used more as a symbol than as an acronym.