Question

Find the angle of incidence so that the incident light ray retraces its path after third reflection.

• A. ${45}^{\circ }$
• B. ${75}^{\circ }$
• C. ${60}^{\circ }$
• D. ${70}^{\circ }$

Answer 1

The correct option is C ${60}^{\circ }$

The light ray will retrace its path after the third reflection if it strikes the inclined plane mirror $M_2$ normally at the point of incidence $\left(P\right)$.


From the concept of geometry, in $△OPN$, $\angle PNO={60}^{\circ }$
So, $\theta ={90}^{\circ }-{60}^{\circ }={30}^{\circ }$
Now, in $△PNM$,
${90}^{\circ }+2\theta +({90}^{\circ }-i)={180}^{\circ }$
$\Rightarrow i=2\theta =2\times {30}^{\circ }={60}^{\circ }$