Question

A light ray parallel to x-axis is incident on a parabolic concave mirror in $XY$ plane. The focus of this parabola is at $(1,0)$. The unit vector along the reflected ray will be

• A. $\hat{j}$
• B. $-\hat{j}$
• C. $\frac{\hat{i}+4\hat{j}}{\sqrt{17}}$
• D. $-\hat{i}$

Answer 1

The correct option is B $-\hat{j}$

After reflection, the reflected ray passes through the focus $F\left(1.0\right)$

Position vector of reflected ray $=(1-1)\hat{i}+(0-4)\hat{j}=\left(0\right)\hat{i}-4\hat{j}$

Its unit vector $=\frac{\left(0\right)\hat{i}-4\hat{j}}{\sqrt{0^2+4^2}}=-\hat{j}$