Question

Two plane mirrors are inclined to each other with their reflecting faces making acute angle. A light ray is incident on one plane mirror. The total deviation after two successive reflections is

• A. independent of the initial angle of incidence
• B. independent of the angle between the mirrors
• C. dependent on the initial angle of incidence
• D. dependent on the angle between the mirrors

Answer 1

Answer: (A), (D)

independent of the initial angle of incidence
dependent on the angle between the mirrors

As indicated in the figure,
If i be the angle of incidence, r be the angle of reflection,
$\delta =\pi -(\pi -2i-2r)$
Hence, $\delta =2i+2r$
Also, using the sum of angles of a triangle, $i+r-\theta =0$
Thus, $\delta =2\theta$
Which means, that the deviation is independent of either the angle of incidence and also the angle of relection. It only depends on the angle between the mirrors