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 at the edge of $A$. The plane of incidence coincides with the plane of the figure. The maximum number of times the ray undergoes reflection (including the first one) before it emerges out is

• A. $28$
• B. $30$
• C. $31$
• D. $32$

Answer 1

The correct option is C $31$

After first reflection, let the reflected ray reach mirror $B$ at distance $x$ from the edge, as shown in figure.


From the figure, we can deduce that
Maximum number of reflections after the first, is given by $\left[\frac{\ell }{x}\right]$, where [] indicates the greatest integer function.

Also, $\tan {30}^{\circ }=\frac{x}{0.2}$
$\Rightarrow x=0.2\times \frac{1}{\sqrt{3}}$

From the data given in the question, $\ell =2\sqrt{3}\text{m}$

$\therefore \left[\frac{\ell }{x}\right]=\frac{2\sqrt{3}}{\frac{0.2}{\sqrt{3}}}=30$

Therefore, total number of reflections (including the first one)
$n=\left[\frac{l}{x}\right]+1=31$
i.e the reflected ray undergoes maximum 31 reflections before it emerges out.