Question

Two plane mirrors are placed perpendicular to each other. A ray of light strikes the first mirror and after reflection from the first mirror it falls on the second mirror. Assuming that the final reflected ray is in the plane of the incident ray, the final reflected ray emerges:

• A. Perpendicular to the original ray
• B. Parallel to the original ray
• C. At ${45}^{\circ }$ to the original ray
• D. At ${60}^{\circ }$ to the original ray

Answer 1

The correct option is B Parallel to the original ray

​​​​​From the figure, it is clearly understood that the ray is emerging out parallel to the original ray. It is valid only when the plane of the final reflected ray and the incident ray are in the same plane.

The original ray incident on the first mirror makes an angle of incidence and angle of reflection of $i^{\circ }$ and an angle of $(90-i{)}^{\circ }$ with the mirror plane.

Using geometrical formulae we can calculate the angle the 2nd ray i.e. the first reflected ray to make $i^{\circ }$ with the second mirror and according to laws of reflection to have an angle of incidence and reflection of $i^{\circ }$ for the second mirror.

The sum of interior angles between the final and original rays is
$i^{\circ }+i^{\circ }+(90-i{)}^{\circ }+(90-i{)}^{\circ }={180}^{\circ }$
Meaning, the original and the final reflected rays are parallel.