Question

A ray parallel to $x$ - axis is incident on a spherical reflecting surface of radius $R$ and the reflected ray becomes parallel to the $y$ - axis as shown. 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 law of reflection:
$\angle i=\angle r$
Since normal at $P$ passes through the centre of the sphere.
So $\angle i+\angle r={90}^{\circ }$
$\angle i=\angle r={45}^{\circ }$
Coordinates of $P=(-R\cos {45}^{\circ },+R\sin {45}^{\circ })$
$=(-\frac{R}{\sqrt{2}},\frac{R}{\sqrt{2}})$