maths formula?

Question

the shutter speed, S, of a camera varies inversley as the square of the appature setting,f.
when f=8,S=125
1. what is the formula for S in terms of f
2.hence, or otherwise calculate the value of S when f=4

Answer 1

S=k*(1/f^2)

Solve for the constant

125=k/(8^2)

k=8000

so the formulat should be S=8000(1/f^2)

when f=4
S=8000/4^2=500

Answer 2

The shutter speed s is inversely proportional to the square root of the aperture setting f, or,

s ~ 1/sqrt(f).

So if you want the exposure to be the same and you reduce the aperture by the square root of 2 (which is 1.4 approx), you double the shutter speed. Thus if the exposure is for f8 and s=125, then your shutter speeds are:

f5.6 shutter 250, (f8/1.4 = 5.6 approx)
f4 shutter 500. (f5.6/1.4 = 4 approx).


Cameras are designed for you to do this easily. If you open the aperture by one stop, you double the shutter speed which is usually the next faster click. The reverse also apply.