Question 364: Ray Optics

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 $	heta$ 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?

Accepted Answer

As we can see, for $$	heta=30^\circ$$, the ray will incident normally and hence will retrace its path.
$$\Rightarrow$$ (A) is correct
Considering the symmetry of the situation, we can have :
$$\Rightarrow$$ (B) is correct
As is clear from the above diagram, ray comes out.
$$\Rightarrow$$ (C) is not correct
Also, as is clear from the above diagram, total number of reflections = 5.
(D) is not correct.

Answer

The ray of light will come out for $	heta=30^{\circ}$, for $0< l < L$.

Answer

There is an angle for $l=\frac{L}{2}$ at which the ray of light will come out after two reflections.

Answer

The ray of light will
NEVER
come out for $	heta=60^{\circ}$, and $l=\frac{L}{3}$.

Answer

The ray of light will come out for $	heta=60^{\circ}$, and $0 < l < \frac{L}{2}$ after six reflections.

Ray Optics

Choose the correct answer: