Question

A ray of light strikes a plane mirror PQ at an angle of incidence of 30°, is reflected from the plane mirror and then strikes a second plane mirror QR placed at right angles to the first mirror. The angle of reflection at the second mirror is:

(a) 30°
(b) 45°
(c) 60°
(d) 90°
Draw a ray-diagram to illustrate your answer.

Answer 1

(c) 60^o


Here,
$$\begin{gathered} \angle \mathrm{ABN}=\angle \mathrm{NBC}(\mathrm{angle}\mathrm{of}\mathrm{incidence}=\mathrm{angle}\mathrm{of}\mathrm{reflection}) \\ \angle \mathrm{BCO}=\angle \mathrm{NBC}(\mathrm{alternate}\mathrm{angles}) \\ \angle \mathrm{MCB}={90}^{\mathrm{O}}-\angle \mathrm{BCO}(\angle \mathrm{MCB}=\mathrm{angle}\mathrm{of}\mathrm{incidence}\mathrm{for}\mathrm{mirror}\mathrm{QR}) \\ ={60}^{\mathrm{o}} \\ \mathrm{Now}, \\ \angle \mathrm{MCB}=\angle \mathrm{MCD}={60}^{\mathrm{o}}(\angle \mathrm{MCD}=\mathrm{angle}\mathrm{of}\mathrm{reflection}\mathrm{from}\mathrm{mirror}\mathrm{QR}\mathrm{and}\mathrm{angle}\mathrm{of}\mathrm{incidence}=\mathrm{angle}\mathrm{of}\mathrm{reflection}) \end{gathered}$$