Question

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 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 time 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)

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,
$\tan 30^{\circ}=\frac{ d }{ 0 . 2 }=\frac{1}{\sqrt{3}}$
or, $d =\frac{ 2 }{ 1 0 \sqrt{ 3 }} m$
The ray will not undergo reflection after it emerges out of the arrangement, i.e., after the ray covers $2 \sqrt{3} m$
Therefore the maximum number of reflections that occur $=\frac{2 \sqrt{3}}{\frac{2}{10 \sqrt{3}}}=30$