question_answer

The separation between the screen and a concave mirror is 2r. An isotropic point source of light is placed exactly midway between the mirror and the point source. Mirror has a radius of curvature r and reflects 100% of the 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: B

Solution :

                   Illuminance on the screen without mirror is \[{{I}_{1}}=\frac{L}{{{r}^{2}}}\] Illuminance on the screen with mirror \[{{I}_{2}}=\frac{L}{{{r}^{2}}}+\frac{L}{{{r}^{2}}}=\frac{2L}{{{r}^{2}}}\] Þ \[\frac{{{I}_{2}}}{{{I}_{1}}}=2:1\]