Question

Two plane mirrors $M_1$ and $M_2$ are inclined to each other at ${70}^{\circ }.$ A ray incident on the mirror $M_1$ at an angle $\theta$ falls on $M_2$ and is then reflected parallel to M, for

• A. $\theta ={45}^{\circ }$
• B. $\theta ={50}^{\circ }$
• C. $\theta ={55}^{\circ }$
• D. $\theta ={60}^{\circ }$

Answer 1

Answer: (B)

$\theta ={50}^{\circ }$

Given,

The angle between the mirrors is ${70}^{\circ }$.

From the figure,

According to the angle sum property of triangle for $\Delta ABC$

$\angle A+\angle B+\angle C={180}^{\circ }$

Hence

${70}^{\circ }+{70}^{\circ }+{90}^{\circ }-{\theta }_i={180}^{\circ }$

${230}^{\circ }-{\theta }_i={180}^{\circ }$

${\theta }_i={50}^{\circ }$