Question

Two plane mirrors A and B are aligned parallel to each as shown in the figure. A light ray is incident at an angle of ${30}^{\circ }$ 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. $34$

Answer 1

The correct option is B $30$

Let the distance covered by the ray after reflection from a surface be $d$.
From the first law of reflection and alternate angle property, all the angles shown in the figure are equal to ${30}^{\circ }$.
From the figure,
$\tan {30}^{\circ }=\frac{d}{0.2}=\frac{1}{\sqrt{3}}$
$d=\frac{2}{10\sqrt{3}}\text{m}$
The ray will not undergo reflection after it emerges out of the arrangement, i.e.,
after the ray covers $2\sqrt{3}\text{m}.$
Therefore, the maximum number of reflections that occur = $\frac{2\sqrt{3}}{\frac{2}{10\sqrt{3}}}=30$.