Question

A ray parallel to the $x-$ axis is incident on a spherical reflecting surface having radius $R$ and the reflected ray becomes parallel to the y - axis as shown in the figure. Find the coordinates of point $P$.

• A. $(-R,R)$
• B. $(\frac{R}{\sqrt{2}},\frac{R}{\sqrt{2}})$
• C. $(-\frac{R}{\sqrt{2}},\frac{R}{\sqrt{2}})$
• D. $(-\frac{R}{2},\frac{R}{2})$

Answer 1

The correct option is C $(-\frac{R}{\sqrt{2}},\frac{R}{\sqrt{2}})$

As per the law of reflection
$\angle i=\angle r$


As, $\angle i+\angle r={90}^{\circ }$
So, $\angle i=\angle r={45}^{\circ }$

Coordinates of point $P$ are thus given as
$P=(-R\cos {45}^{\circ },+R\sin {45}^{\circ })$
$=(\frac{-R}{\sqrt{2}},\frac{R}{\sqrt{2}})$