Question

Figure shows a square enclosure, The inner surfaces are plane mirrors. A ray of light enters a small hole in the centre of one mirror. At what angle $\theta$ must the ray enter in order to exit through the hole after being reflected one by each mitrors?

• A. ${15}^{\circ }$
• B. ${30}^{\circ }$
• C. ${45}^{\circ }$
• D. None of these

Answer 1

The correct option is C ${45}^{\circ }$

For the light ray to exit the small hole the final angle of reflection must be equal to the first angle of incidence. In order to exit the hole the ray must struck the sides of the square at their midpoints.

Let the side of the square be $l$.

The ray strikes at $\frac{l}{2}.$

Hence, $\tan \theta =\frac{l/2}{l/2}=1$

Or $\theta ={45}^{\circ }$

Hence the correct answer is option (C).