Editing F-number (section)

== Notation ==

The f-number {{mvar|N}} is given by:

<math display=block>N = \frac{f}{D} \ </math>

where {{mvar|f}} is the [[focal length]], and {{mvar|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's diameter in terms of {{mvar|f}} and {{mvar|N}}.<ref name="ReferenceA"/> For example, if a [[Lens (optics)|lens's]] focal length were {{val|100|u=mm}} and its entrance pupil's diameter were {{val|50|u=mm}}, the f-number would be 2. This would be expressed as {{nowrap|"{{f/|2}}"}} in a lens system. The aperture diameter would be equal to {{math|''f''/2}}.

Camera lenses often include an adjustable [[diaphragm (optics)|diaphragm]], which changes the size of the [[aperture stop]] and thus the entrance pupil size. This allows the user to vary the f-number as needed. 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.

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. A {{val|100|u=mm}} focal length {{f/|4}} lens has an entrance pupil diameter of {{val|25|u=mm}}. A {{val|100|u=mm}} focal length {{f/|2}} lens has an entrance pupil diameter of {{val|50|u=mm}}. Since the area is proportional to the square of the pupil diameter,<ref>See [[Area of a circle]].</ref> the amount of light admitted by the {{f/|2}} lens is four times that of the {{f/|4}} lens. To obtain the same [[Exposure (photography)|photographic exposure]], the exposure time must be reduced by a factor of four.

A {{val|200|u=mm}} focal length {{f/|4}} lens has an entrance pupil diameter of {{val|50|u=mm}}. The {{val|200|u=mm}} lens's entrance pupil has four times the area of the {{val|100|u=mm}} {{f/|4}} 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 {{val|100|u=mm}} lens, the {{val|200|u=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.