Question

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

• 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)

$- \frac { 1 } { 3 } , - \frac { 2 } { 3 } , \frac { 2 } { 3 }$

Answer 2

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

$\frac { 1 + \ell } { 2 \cos \theta } = \frac { 1 } { \sqrt { 3 } }$ , $\frac { 0 + m } { 2 \cos \theta } = - \frac { 1 } { \sqrt { 3 } }$ and $\frac { 0 + n } { 2 \cos \theta } = \frac { 1 } { \sqrt { 3 } }$

⇒ l = – $\frac { 1 } { 3 }$ , m = – $\frac { 2 } { \sqrt { 3 } }$, n = $\frac { 2 } { 3 }$