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)

0.02 s

Answer 2

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 $\frac{1}{200\,{{T}_{2}}}={{\left( \frac{2.8}{5.6} \right)}^{2}}$ 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 $f/1.5.$