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Equation / Last modified by mike on 2015/07/29 07:16

This equation computes the f-stop or f-number of an optical system. 

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 or aperture. It is a dimensionless number that is a quantitative measure of lens speed, and an important concept in photography. 1

InputsThe focal point F and focal length f of a positive (convex) lens, a negative (concave) lens, a concave mirror, and a convex mirror (mod).png  2

  • - focal length.  The focal length of an optical system is a measure of how strongly the system converges or diverges light.
  • D - diameter of the effective aperture


It is customary to write f-numbers preceded by f/. For example, if a lens's focal length is 10 mm and its aperture diameter is 5 mm, the f-number is 2 and is written f/2.

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.

Many camera lenses have an adjustable diaphragm, which changes the size of the aperture and thus the entrance pupil size. The entrance pupil diameter is not necessarily equal to the aperture 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.


  1. ^ http://en.wikipedia.org/wiki/F-number
  2. ^ IMAGE:"Focal-length" by Henrik - Own work. Licensed under CC BY-SA 3.0 via Wikimedia Commons - http://commons.wikimedia.org/wiki/File:Focal-length.svg#mediaviewer/File:Focal-length.svg