Question

Two plane mirrors AB and BC are inclined at angle $\theta$ as shown in figure. If mirror AB is horizontal and emergent ray after two reflections is vertical, then $\theta$ is

• A. ${135}^{\circ }$
• B. ${105}^{\circ }$
• C. ${115}^{\circ }$
• D. ${120}^{\circ }$

Answer 1

The correct option is B ${105}^{\circ }$


$\theta +\alpha ={120}^{\circ }\dots \dots \dots \left(1\right)$

$\pi -\theta +\alpha =\frac{\pi }{2}$

$\theta -\alpha ={90}^{\circ }\dots \dots \dots \left(2\right)$

By (1) + (2)

$\theta ={105}^{\circ }$