fnumret

The f-number, denoted by N and written as f/number, is the ratio of a lens’s focal length to the diameter of its entrance pupil. It is a dimensionless quantity used in photography and optics to describe how large the lens’s aperture appears relative to its focal length.

Specifically, N = f / D. A smaller N means a larger entrance pupil, which gathers more light and produces a brighter image, but also a shallower depth of field. A larger N reduces light and increases depth of field.

Exposure and stops: For a given scene, image brightness is proportional to 1/N^2. Each full stop change (for example from f/4 to f/5.6) halves or doubles the light reaching the sensor.

Depth of field and application: Depth of field depends on N, focal length, distance to the subject, and circle of confusion. Narrow apertures yield greater DOF; wide apertures yield shallower DOF. Photographers balance exposure, DOF, and sharpness by choosing aperture, distance, and focal length to achieve the desired composition and focus.

Variants and terminology: In motion pictures, T-stops account for lens transmission. The f-number describes potential light transmission, but two lenses with the same f-number may transmit different amounts of light due to coatings, glass, and design.

History and terminology: The f-number concept emerged in early 20th-century lens design and is standard across still photography and cinematography. It remains a central parameter for shaping exposure and depth of field in optical imaging.