question_answer

The separation between the screen and a plane mirror is 2r. An isotropic point source of light is placed exactly midway between the mirror and the screen. Assume that mirror reflects 100% of incident light. Then the ratio of illuminances on the screen with and without the mirror is

A)            10 : 1                                        

B)            2 : 1

C)            10 : 9                                        

D)            9 : 1

Correct Answer: C

Solution :

                   The illuminance on the screen without mirror is \[{{I}_{1}}=\frac{L}{{{r}^{2}}}\] The illuminance on the screen with mirror is \[{{I}_{2}}=\frac{L}{{{r}^{2}}}+\frac{L}{{{(3r)}^{2}}}=\frac{10}{9}\times \frac{L}{{{r}^{2}}}\] \[\therefore \frac{{{I}_{2}}}{{{I}_{1}}}=\frac{10}{9}=10:9\]