Question

Two plane mirrors are inclined at ${70}^{\circ }$. A ray incident on one mirror at an angle $\theta$ after reflection falls on the second mirror and is reflected from there parallel to the first mirror, then the angle $\theta$ is

• A. ${50}^{\circ }$
• B. ${45}^{\circ }$
• C. ${30}^{\circ }$
• D. ${55}^{\circ }$

Answer 1

The correct option is A ${50}^{\circ }$


From the figure we can clearly see that ${20}^{\circ }$ is the angle of reflection with respect to the normal $N_2$ at mirror $M_2$.
Therefore from law of reflection,
$\angle i=\angle r$
Hence ${20}^{\circ }$ is the angle of incidence for light ray incident at $M_2$ after getting reflected from $M_1$
From the triangle formed by both mirrors and reflected ray at $M_1$,
$\Rightarrow {70}^{\circ }+{70}^{\circ }+({90}^{\circ }-\theta )={180}^{\circ }$
$\therefore \theta ={50}^{\circ }$