Question

The diagram in figure shows an incident ray $\text{AO}$ and the reflected ray $\text{OB}$ from a plane mirror.The angle $\text{AOB}\text{is}{30}^{\circ }$. Draw normal on the plane mirror at point $\text{O}$ and find the angle of reflection.

Answer 1

$\text{ON}$ is normal on the plane mirror at point $O$.
Angle of incidence $\angle i=\angle \text{AON}$
Angle of reflection $\angle r=\angle \text{BON}$
According to law of reflection,
$\angle i=\angle r$
Given, $\angle \text{AOB}={30}^{\circ }$
$\angle \text{AON}+\angle \text{BON}={30}^{\circ }$
$\angle i+\angle r={30}^{\circ }$
$\angle r+\angle r={30}^{\circ }$
$2\angle r={30}^{\circ }$
$\angle r=\frac{{30}^{\circ }}{2}$
$\angle r={15}^{\circ }$
Therefore, the angle of reflection angle is ${15}^{\circ }$