Question

A ray PO is incident on the mirror AC at an angle ${30}^{\circ }$ as shown in the figure Ray PO is reflected by mirror AB and AC the deviation of ray PO after its final reflection from mirror AC is $K\pi$ Find the value of K

Answer 1

Given : $i={30}^o$

Using $i=r$, we get $r=\angle MON={30}^o$

As OM is a normal, thus $\angle MOA={90}^o$ $⟹\angle NOA={90}^o-{30}^o={60}^o$

Hence triangle $ONA$ is a right angled triangle as shown in the figure.

From figure, a ray after being reflected from mirror AC falls normally on mirror

AB and hence bounce back tracing its original path. So the ray is finally

reflected by ${180}^o$.

$⟹K=1$