Question

Two plane mirror A and B are oriented perpendicular to each other. A light ray incident at angle $\theta$ on mirror A is also reflected by the mirror B. If the reflected ray from mirror B is parallel to the incident ray on A, such that the ray reflected from the first mirror as the same angle of incidence on the second mirror then find the value of $\theta$.

Answer 1

It is given $i_1=i_2$

And from figure $i_2=90-\theta$

And from laws of reflection $r_1=i_1=90-\theta$

Hence $x=90-r_1=\theta$

And since $i_2=i_1=90-\theta$

Hence $y=90-i_2=\theta$

so from triangle

${90}^0+x+y={180}^0$

$2\theta ={90}^0$

$\theta ={45}^0$