Question

Two plane mirrors each $14\text{m}$ long are facing each other as shown in the figure. The distance between the mirrors is $\sqrt{3}\text{m}$. A light ray is incident at the corner end of one of the mirrors at an angle of incidence ${30}^{\circ }$. How many times does the ray gets reflected before it reaches the other corner end of the either mirrors?

• A. $14$
• B. $10$
• C. $12$
• D. $18$

Answer 1

The correct option is A $14$

The ray diagram for reflection of light incident at the corner end of one of the mirrors is shown in the figure.

Let us suppose, the distance moved by light ray after first reflection along the mirror is $d$.
From the geometry,
$\tan {30}^{\circ }=\frac{d}{\sqrt{3}}$
$\Rightarrow \frac{1}{\sqrt{3}}=\frac{d}{\sqrt{3}}$
$\Rightarrow d=1\text{m}$
So, number of reflections of light ray before it reaches the other corner end of the either mirrors,
$n=$ length of mirror $/$ distance moved along mirror by light ray in one reflection
$\Rightarrow n=\frac{14}{1}=14$