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F-stop

Numbers corresponding to the variable size of the camera's iris opening, and thus amount of light passing through the lens. The higher the number, the less light enters.
Aperture Diagram

The f-number of an optical system (such as a camera lens) is the ratio of the system's focal length to the diameter of the entrance pupil ("clear aperture"). It is a dimensionless number that is a quantitative measure of lens speed, and an important concept in photography. It is also known as the focal ratio, f-ratio, or f-stop. It is the reciprocal of the relative aperture. The f-number is commonly indicated using a hooked f with the format f/N, where N is the f-number.

The f-number N is given by:

N = f D {\displaystyle N={\frac {f}{D}}\ } N={\frac {f}{D}}\

where f {\displaystyle f} f is the focal length, and D {\displaystyle D} D is the diameter of the entrance pupil (effective aperture). It is customary to write f-numbers preceded by f/, which forms a mathematical expression of the entrance pupil diameter in terms of f and N. For example, if a lens's focal length is 10 mm and its entrance pupil diameter is 5 mm, the f-number is 2, expressed by writing "f/2", and the aperture diameter is equal to f / 2 {\displaystyle f/2} f/2, where f {\displaystyle f} f is the focal length.

Ignoring differences in light transmission efficiency, a lens with a greater f-number projects darker images. The brightness of the projected image (illuminance) relative to the brightness of the scene in the lens's field of view (luminance) decreases with the square of the f-number. Doubling the f-number decreases the relative brightness by a factor of four. To maintain the same photographic exposure when doubling the f-number, the exposure time would need to be four times as long.

Most lenses have an adjustable diaphragm, which changes the size of the aperture stop and thus the entrance pupil size. The entrance pupil diameter is not necessarily equal to the aperture stop diameter, because of the magnifying effect of lens elements in front of the aperture.

A 100 mm focal length f/4 lens has an entrance pupil diameter of 25 mm. A 200 mm focal length f/4 lens has an entrance pupil diameter of 50 mm. The 200 mm lens's entrance pupil has four times the area of the 100 mm lens's entrance pupil, and thus collects four times as much light from each object in the lens's field of view. But compared to the 100 mm lens, the 200 mm lens projects an image of each object twice as high and twice as wide, covering four times the area, and so both lenses produce the same illuminance at the focal plane when imaging a scene of a given luminance.

A T-stop is an f-number adjusted to account for light transmission efficiency.

Key Terms

brightness
diameter
entrance pupil
entrance pupil diameter
f number
focal length
lens
mm
mm lens
times

Additional Resources

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Acronymn

(none found)

Synonymns

F-stop
F-number
F-ratio
Focal ratio

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Sources & Credits

Last modified on September 13 2019
Content adapted from Wikipedia
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