Question

The plane mirrors $A$ and $B$ are aligned parallel to each other, as shown in the figure. A light ray is incident at an angle ${30}^o$ at a point just inside one end of $A$. The place 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. $34$

Answer 1

Answer: (B)

$30$

According to laws of reflection

$\angle i=\angle r$

So,

$\angle PQO={30}^0$

Given,

$PQ=0.2m$

$tan\theta =\frac{OP}{PQ}$

$⟹\frac{1}{\sqrt{3}}=\frac{OP}{0.2}$

$⟹OP=\frac{0.2}{\sqrt{3}}m$

$OP$ is the distance covered by the ray on one rflection.

Number of times the ray undergoes reflection, before it emerges out $=\frac{2\sqrt{3}}{OP}=\frac{2\sqrt{3}}{0.2/\sqrt{3}}=\frac{6}{0.2}=30$