Question

Two plane mirrors A and B are aligned parallel to each other, as shown in figure. A light ray is incident at an angle $30$ 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. $34$

Answer 1

The correct option is B $30$

no. of reflection $=\frac{2\sqrt{3}}{x}$

as $x=$ length occupied by ray in 1 reflection & we have $2\sqrt{3}$ as total length.

$\Rightarrow \tan {30}^{\circ }=\frac{x}{0.2}$

$\Rightarrow \frac{1}{\sqrt{3}}=\frac{x}{0.2}\Rightarrow \frac{0.2}{\sqrt{3}}=x$

0. total no. of reflection $=\frac{2\sqrt{3}}{x}=\frac{2\sqrt{3}}{\frac{0.2}{\sqrt{3}}}=\underset{–}{30}$

Hence option 'B) is correct