question_answer

The intensity of a point source of light, S, placed at a distance d in front of a screen A, is \[{{I}_{0}}\] at the center of the screen. Find the light intensity at the center of the screen if a completely reflecting plane mirror M is placed at a distance d behind the source, as shown in figure.

A) \[\frac{27\,{{I}_{0}}}{9}\]        

B) \[\frac{25\,{{I}_{0}}}{9}\]

C) \[\frac{17\,{{I}_{0}}}{9}\]        

D) \[\frac{10\,{{I}_{0}}}{9}\]

Correct Answer: D

Solution :

[d] \[{{E}_{1}}={{I}_{0}}=\frac{L}{{{d}^{2}}}\], without mirror And \[{{E}_{2}}=\frac{L}{{{d}^{2}}}+\frac{L}{{{(3d)}^{2}}}=\frac{L}{{{d}^{2}}}\left[ 1+\frac{1}{9} \right]=\frac{10{{I}_{0}}}{9}\] with mirror.