Camera A has a lens with an aperture diameter of 830 mm It

Camera A has a lens with an aperture diameter of 8.30 mm . It photographs an object using the correct exposure time of 3.33×102 s .

A. What exposure time should be used with camera B in photographing the same object with the same film if this camera has a lens with an aperture diameter of 22.9 mm ? The lenses of cameras A and B have the same focal length.

Solution

r_a = 8.30 / 2 = 4.15

r_b = 22.9 / 2 = 11.45

t_b * A_b = t_a * A_a

t_b / t_a = A_a / A_b = (r_a / r_b)²

t_b = t_{a *} (r_a / r_b)²

= 3.33 * 10^-2 * [4.15² / 11.45²]

= 4.37 * 10^-3 s