Question

What should be angle such that ray coming parallel to mirror Retract its own path.

• A. 0°
• B. 45°
• C. 90°
• D. 180°

Answer 1

Answer: (C)

90°

Answer 2

For a ray to retrace its path after reflection from two mirrors inclined at an angle $\theta$, it must be incident normally on the last mirror it encounters.

If an incident ray is parallel to one mirror (say M1) and strikes the other mirror (M2), for it to retrace its path, the reflected ray from M2 must be incident normally on M1.

Let the angle between the mirrors be $\theta$. If the incident ray is parallel to M1, its angle with M2 is $\theta$. So, the angle of incidence on M2 is $i_2 = \theta$. The angle of reflection from M2 is $r_2 = \theta$.

The angle of the reflected ray from M2 with respect to M1 depends on the orientation. For the ray to be incident normally on M1, its angle with M1 must be $90^\circ$.

A detailed analysis shows that this condition is met when the angle between the mirrors $\theta$ is $90^\circ$. In this case, if a ray is incident parallel to one mirror, it strikes the second mirror normally, reflects back along its path, and thus retraces its path.