Question

A reflecting surface is represented by the equation $x^2+y^2=a^2$. A ray travelling in negative x-direction is deviated towards positive y-direction after reflection from the surface at point $P$. Then co-ordinates of point $P$ are

• A. $(0.8a,0.6a)$
• B. $(0.6a,0.8a)$
• C. $(\frac{a}{2},\frac{a}{2})$
• D. None of these

Answer 1

The correct option is D None of these

Given mirror is circular in nature, so normal passes throught origin.
As after reflection ray moves along y axis
$i+r={90}^{\circ }$
for reflection
$i=r$
$\Rightarrow 2i={90}^{\circ }\Rightarrow i=r={45}^{\circ }$

The ray diagram is as shown.

​​​​​​​For point $P$
$x=\frac{a}{\sqrt{2}}$ and $y=\frac{a}{\sqrt{2}}$
$\therefore P=(\frac{a}{\sqrt{2}},\frac{a}{\sqrt{2}})$