Question

A ray of light parallel to $x-$axis is incident on a circle $(x-2{)}^2+y^2=4^2$ polished from inside as shown in the figure. Find the co-ordinate of $x\text{and}y$ w.r.t origin of the point at which the incident ray parallel to $x-$axis should fall such that the reflected ray deviated by ${60}^{\circ }$ after reflection.

• A. $(x,y)=(-2,2\sqrt{3})$
• B. $(x,y)=(2,2\sqrt{3})$
• C. $(x,y)=(0,2\sqrt{3})$
• D. $(x,y)=(0,0)$

Answer 1

The correct option is C $(x,y)=(0,2\sqrt{3})$

As per the given equation of circle, the center of the circle is at $(2,0)$ and its radius is $4$
So, the given situation can be shown as
So, here from the geometry we can say that the co-ordinates are
$(x,y)=(R\cos {60}^{\circ }-2,R\sin {60}^{\circ })$
$\Rightarrow (x,y)=(4\cos {60}^{\circ }-2,4\sin {60}^{\circ })$
$\Rightarrow (x,y)=(0,2\sqrt{3})$