Question

Two plane mirrors are inclined to each other at an angle of ${70}^0$. A ray is incident on one mirror at an angle $\theta$. The ray reflected from this mirror falls on the second mirror from where it is reflected parallel to the first mirror. Determine the value of $\theta$.

• A. $\theta ={70}^0$
• B. $\theta ={45}^0$
• C. $\theta ={50}^0$
• D. $\theta ={40}^0$

Answer 1

The correct option is C $\theta ={50}^0$

$\angle I=\theta$

$\angle r=\theta$ for first mirror

Angle between the reflected ray and the first mirror will be $\angle 90-\theta$

Angle between the two mirrors = ${70}^o$

Since the emergent ray comes out parallel to the first mirror, it also makes ${70}^o$ with the second mirror. Thus $\angle e$= angle of reflection for second mirror= $90-70={20}^o$

The reflected ray from first mirror, striking the second mirror makes a triangle with the two mirrors. Angle of incidence of 2nd mirror= angle of incidence for 2nd mirror= ${20}^o$

Thus the angle between the reflected ray from first mirror and the second mirror= 90-20= ${70}^o$

Since, it makes a triangle, $180=70+70+(90-\theta )$

$\theta ={50}^o$