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Q.
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:
Bihar CECEBihar CECE 2005Ray Optics and Optical Instruments
Solution:
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. $