Question

The exposure time of a camera lens at $f/2.8$ setting is $1/200$ s. The correct exposure time at $f/5.6$ setting is:

• A. 0.02 s
• B. 0.04 s
• C. 0.20 s
• D. 0.40 s

Answer 1

Answer: (A)

The exposure time of camera lens is given by
Time of exposure $\propto \frac{1}{{(Aperture)}^2}$
Also, $-\text{number}=\frac{\text{Focal}\text{length}\text{(f)}}{\text{Aperture}\text{(A)}}$
or $\text{Aperture}\text{(A)}=\frac{\text{Focal}\text{length}(f)}{f-number}$
Therefore, $\frac{T_1}{T_2}=\frac{A_2}{A_1}$
Given, $T_1=\frac{1}{200},A_1=\frac{f}{2.8},A_2=\frac{f}{5.6}$
$\therefore$ $\frac{1/200}{T_2}={\left(\frac{f/5.6}{f/2.8}\right)}^2$
or $\frac{1}{200T_2}={\left(\frac{2.8}{5.6}\right)}^2$
or $T_2={\left(\frac{5.6}{2.8}\right)}^2\times \frac{1}{200}$
Note: Smaller the f-number larger will be the aperture and lesser will be the time of exposure and faster will be the camera. This is why movie cameras have very low $f.$ numbers such as $f/1.5.$