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.