A View of Mathematics Through A Camera Lens
by Donald M. Fairbairn
Consider the operation of a camera lens:
Observe that as d decreases (the lens closes), then f increases.
Now the amount of light admitted depends on the area of the aperture, which in turn depends on d.
,
and since and
.
For a standard 50 mm, l = 50 mm, so for f = 1.4, and
for f = 2, . Observe that . This pattern will continue. The area is halved at each successive f-stop. Now if A is halved each time, then is doubled. Hence f is multiplied by . Thus, the f-stop numbers represent this progression:
,
which is a geometric sequence!
The amount of light that enters a camera is determined by the f-stop setting of the lens. The commonly used f-stop numbers are 1, 1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22, 32, and 45.