Question

The convex reflecting surface (silvered on the right side) is represented by the equation $2x=y^2$ as shown in figure. A ray travelling horizontally along positive x-axis becomes vertical after reflection The co-ordinates of the point of incidence can be

• A. $(\frac{1}{2},1)$
• B. $(1,\frac{1}{2})$
• C. $(\frac{1}{2},\frac{1}{2})$
• D. $(-\frac{1}{2},-1)$

Answer 1

The correct option is A $(\frac{1}{2},1)$


$i=r={45}^{\circ },\theta ={45}^{\circ }$
$tan{45}^{\circ }=\frac{dy}{dx}$
$1=\frac{2}{2\sqrt{2x}}$
$\Rightarrow x=\frac{1}{2}$
$y=\sqrt{2\times \frac{1}{2}}=1$
Thus $x,y)=(\frac{1}{2},1)$