Question

Two plane mirrors, $\text{A}$ and $\text{B}$ 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 $\text{A}.$ 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 $30$


From the ray diagram,

$d=0.2\tan {30}^{\circ }=\frac{0.2}{\sqrt{3}}$

Where, $d=\text{Distance covered by the ray in one reflection}$

Then, no. of reflection it undergoes before emerging out,

$\Rightarrow N=\frac{l}{d}=\frac{2\sqrt{3}}{\left(\frac{0.2}{\sqrt{3}}\right)}=30$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(B\right)$ is the correct answer.