# Working f-Number

## Description

In optics, the f-number (sometimes called focal ratio, f-ratio, f-stop, or relative aperture) of an optical system is the ratio of the lens’s focal length to the diameter of the entrance pupil. It is a dimensionless number that is a quantitative measure of lens speed, and an important concept in photography. The number is commonly notated using a hooked f, i.e. f/N, where N is the f-number.

The f-number accurately describes the light-gathering ability of a lens only for objects an infinite distance away. This limitation is typically ignored in photography, where objects are usually not extremely close to the camera, relative to the distance between the lens and the film. In optical design, an alternative is often needed for systems where the object is not far from the lens. In these cases the working f-number is used. A practical example of this is, that when focusing closer, the lens’ effective aperture becomes smaller, from e.g. f/22 to f/45, thus affecting the exposure.

The working f-number is given by the formula shown here.

Related formulas## Variables

N_{w} | working f-number (dimensionless) |

NA_{i} | image-space numerical aperture of the lens (dimensionless) |