Question

In the given figure, a ray OA is incident upon a smooth surface POQ. It is reflected back along OB. A normal ON is drawn perpendicular to the surface at O (the point of incidence). The value of $\angle AOP$ is ${60}^{\circ }$ . Find the value of the angle of reflection.

• A. ${30}^{\circ }$
• B. ${40}^{\circ }$
• C. ${60}^{\circ }$
• D. ${45}^{\circ }$

Answer 1

The correct option is A

${30}^{\circ }$

$\angle AOP+\angle AON={90}^{\circ }$ (as ON is perpendicular to POQ)

$\Rightarrow \angle AON={90}^{\circ }-{60}^{\circ }$​ (as $\angle AOP={60}^{\circ }$​ )
$\Rightarrow \angle AON={30}^{\circ }$

Now, $\angle AON=\text{angle of incidence}$$=\text{angle of reflection}=\angle BON$

Thus, angle of reflection $={30}^{\circ }$