Editing F-number (section)

== Working f-number ==<!-- This section header is used in redirects -->
The f-number accurately describes the light-gathering ability of a lens only for objects an infinite distance away.<ref name="Greivenkamp">{{cite book | first=John E. | last=Greivenkamp | year=2004 | title=Field Guide to Geometrical Optics | publisher=SPIE | others=SPIE Field Guides vol. '''FG01''' | isbn=0-8194-5294-7 }} p. 29.</ref> This limitation is typically ignored in photography, where f-number is often used regardless of the distance to the object. In [[optical design]], an alternative is often needed for systems where the object is not far from the lens. In these cases the '''working f-number''' is used. The working f-number {{mvar|N<sub>w</sub>}} is given by:<ref name="Greivenkamp"/>

<math display=block>N_w \approx {1 \over 2 \mathrm{NA}_i} \approx \left(1+\frac{|m|}{P}\right)N\,,</math>

where {{mvar|N}} is the uncorrected f-number, {{math|NA<sub>''i''</sub>}} is the image-space [[numerical aperture]] of the lens, <math>|m|</math> is the [[absolute value]] of the lens's [[magnification]] for an object a particular distance away, and {{mvar|P}} is the [[pupil magnification]]. Since the pupil magnification is seldom known it is often assumed to be 1, which is the correct value for all symmetric lenses.

In photography this means that as one focuses closer, the lens's effective aperture becomes smaller, making the exposure darker. The working f-number is often described in photography as the f-number corrected for lens extensions by a [[bellows factor]]. This is of particular importance in [[macro photography]].