Question

Show that if a ray of light is reflected successively from two mirrors inclined at an angle q, the deviation of the ray does not depend upon the angle of incidence.

Answer 1

If $d_1$ and $d_2$ are the deviations suffered at $M_1$ and $M_2$ respectively.

Then $d_1$ = $\pi$ – 2i and $d_2$ = $\pi$ – 2i`

Total deviation, d = 2$\pi$ – 2(i + i`)

From triangle OAB, $\theta$ + $\frac{\pi }{2}$ - i` + $\frac{\pi }{2}$ – i = $\pi$ or $\theta$ = i` + i

Therefore, d = 2$\pi$ - 2$\theta$

Thus, the total deviation is independent of angle of incidence.