Question

A mirror and a source of light are situated at the origin O and at a point on OX respectively. A ray of light from the source strikes the mirror and is reflected. If the direction ratios of the normal to the plane are 1, -1, 1, then direction cosines of the reflected rays are

• A. $\frac{1}{3},\frac{2}{3},\frac{2}{3}$
• B. $-\frac{1}{3},\frac{2}{3},\frac{2}{3}$
• C. $-\frac{1}{3},\frac{2}{3},-\frac{2}{3}$
• D. $-\frac{1}{3},-\frac{2}{3},\frac{2}{3}$

Answer 1

Answer: (D)

Let the ray of light comes along x-axis and strikes the mirror at the origin.
Direction cosines of normal are
$\frac{1}{\sqrt{3}},-\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}}$ so. $cos\frac{\theta }{2}=\frac{1}{\sqrt{3}}$
Let the reflected ray has direction cosines l, m, n then
$\frac{l+1}{2cos\frac{\theta }{2}}=-\frac{1}{\sqrt{3}}\Rightarrow l=\frac{2}{3}-1=-\frac{1}{3}$
$\frac{m+0}{2cos\frac{\theta }{2}}=-\frac{1}{\sqrt{3}}\Rightarrow m=-\frac{2}{3}\frac{n+0}{2cos\frac{\theta }{2}}=\frac{1}{\sqrt{3}}\Rightarrow n=\frac{2}{3}$