Question

Three plane mirrors form an equilateral triangle with each side of length $L$. There is a small hole at a distance $l>0$ from one of the corners as shown in the figure. A ray of light is passed through the hole at an angle $\theta$ and can only come out through the same hole. The cross section of the mirror configuration and the ray of light lie on the same plane.

Which of the following statement(s) is(are) correct?

• A. The ray of light will come out for $\theta=30^{\circ}$, for $0< l< L$.
• B. There is an angle for $l=\frac{L}{2}$ at which the ray of light will come out after two reflections.
• C. The ray of light will NEVER come out for $\theta=60^{\circ}$, and $l=\frac{L}{3}$.
• D. The ray of light will come out for $\theta=60^{\circ}$, and $0< l< \frac{L}{2}$ after six reflections.

Answer 1

Answer: (A), (B)

(A) Ray will come out after one reflection for $\theta=30^{\circ} \& 0< \ell< L$


for $\theta=60^{\circ} \& \ell=\frac{ L }{2}$, ray will come out after two reflections.
(C) For $\ell=\frac{L}{3} \& \theta=60^{\circ}$ ray will come out after five reflections.

(D) For $\theta=60^{\circ} \& 0< \ell< \frac{L}{2}$, ray will come out after five reflections