Question

Two mirrors are inclined at an angle $\theta$ as shown in the figure. Light ray is incident parallel to one of the mirrors. Light will start retracing its path after the third reflection if-

• A. $\theta ={45}^{\circ }$
• B. $\theta ={30}^{\circ }$
• C. $\theta ={60}^{\circ }$
• D. All three

Answer 1

The correct option is B $\theta ={30}^{\circ }$




From $△ABC$ we get,

${90}^{\circ }+2\theta +{90}^{\circ }-i={180}^{\circ }......\left(1\right)$

Also, $i={90}^{\circ }-\theta$

From (1) we get,

${90}^{\circ }+2\theta +\theta ={180}^{\circ }$

$\therefore \theta ={30}^{\circ }$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(B\right)$ is the correct answer.