Question

A ray of light is coming along the line $x=2$ from positive direction of $y-$axis & strikes a concave mirror whose intersection with the $XOY$ plane is a parabola $x^2=4y$, then equation of the reflected ray after the second reflection is

• A. $y+2=0$
• B. $y+1=0$
• C. $x+2=0$
• D. None of these

Answer 1

Answer: (C)

$x+2=0$

Given equation of parabola is $x^2=4y=4\left(1\right)y$
$\therefore$ Focus $(0,1)$ and the point of intersection of
$x=2$ & parabola $x^2=4y$ is $(2,1)$
Now equation of the first reflection is $y=1$ which is ${\perp }^{er}$ to the incident ray hence second reflected ray is parallel to incident ray & passes through the point $(-2,1)$

The equation after second reflection is $x=-2$ i.e., $x+2=0$
Hence choice (c) is correct answer.