question_answer

Two plane mirrors A and B are aligned parallel to each other as shown in the figure. A light ray is incident at an angle \[30{}^\circ \] at a point just inside one end of A. The plane of incidence coincides with the plane of the figure. The maximum number of times the ray undergoes reflections (including the first one), before it emerges out, is

A) 28                    

B) 30                    

C) 32                    

D) 34

Correct Answer: B

Solution :

According to laws of reflection, \[\angle i=\angle r\] So, \[\angle PQO={{30}^{o}}\] Given, \[PQ=0.2\,m\] \[\tan {{30}^{o}}=\frac{OP}{PQ}\] \[\Rightarrow \]   \[\frac{1}{\sqrt{3}}=\frac{OP}{0.2}\Rightarrow OP=\frac{0.2}{\sqrt{3}}m\] OP is distance covered by the ray in one reflection.

Number of times the ray undergoes reflections, before it emerges out \[=\frac{2\sqrt{3}}{OP}=\frac{2\sqrt{3}}{\frac{0.2}{\sqrt{3}}}=\frac{6}{0.2}=30\]