A plane mirror is placed at the origin so that the direction ratios of its normal are 1, –1, 1. A ray of light, coming along the positive direction of the x-axis, strikes the mirror. The direction cosines of the reflected ray are
Answer & explanation
Correct answer: option 4
If θ is the angle between the normal to the plane and the incident ray, then $cos θ = \frac{1}{\sqrt{3}}$.
If l, m, n are the d.c of the reflected ray, then
$\frac{1+l}{2cosθ}=\frac{1}{\sqrt{3}},\frac{0+m}{2cosθ}=-\frac{1}{\sqrt{3}},\frac{0+n}{2cosθ}=\frac{1}{\sqrt{3}}$
$⇒l=-\frac{1}{3},m=-\frac{2}{3},n=\frac{2}{3}$.
Hence (D) is the correct answer.