Question

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

• A. $\theta = 4 5^{\circ }$
• B. $\theta = 3 0^{\circ }$
• C. $\theta = 6 0^{\circ }$
• D. All three

Answer 1

Answer: (B)

$\alpha =\frac{\left(9 0 - \theta \right)}{2},\left(\alpha \right)_{1}=90-\alpha $ and also,
$\left(\alpha \right)^{1} = 9 0 - \theta = 9 0 - \left(\frac{9 0 - \theta }{2}\right)$
$9 0 - \theta = 4 5 + \frac{\theta }{2}$
$4 5 = \frac{3 \theta }{2}$
$\theta = 3 0^{\circ }$