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Concept
F-number
Summary
An f-number is a measure of the light-gathering ability of any optical system like a camera lens or even the human eye. It is calculated by dividing the system's focal length by the diameter of the entrance pupil. The f-number is also known as the focal ratio, f-ratio, or f-stop, and it is key in determining the depth of field, rate of light scattering, and exposure of a photograph. The f-number is dimensionless that is usually expressed using a lower-case hooked f with the format N, where N is the f-number.
The f-number can also be known as the inverse of the relative aperture (the aperture diameter divided by focal length). The relative aperture indicates how much light can pass through the lens at a given focal length. A lower f-number means a larger relative aperture and more light entering the system, while a higher f-number means a smaller relative aperture and less light entering the system. The f-number is related to the numerical aperture of the system, which measures the range of angles over which light can enter or exit the system. The numerical aperture takes into account the refractive index of the medium in which the system is works, while the f-number does not.
The f-number N is given by:
where is the focal length, and is the diameter of the entrance pupil (effective aperture). It is customary to write f-numbers preceded by "", which forms a mathematical expression of the entrance pupil's diameter in terms of and N. For example, if a lens's focal length were 10 mm and its entrance pupil 's diameter were 5 mm, the f-number would be 2. This would be expressed as "2" in a lens system and the aperture diameter would be equal to .
Most lenses have an adjustable diaphragm, which changes the size of the aperture stop and thus the entrance pupil size. This allows the maker to vary the f-number, according to needs. Note that the entrance pupil diameter is not necessarily equal to the aperture stop diameter, because of lens elements magnify things in front of that small opening.
Official source
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