Question

Two plane mirrors are inclined at angle ${}^{\prime }{\theta }^{\prime }$ as shown in figure. If a ray parallel to OB strikes the other mirror at $P$ and finally emerges parallel to OA after two reflections the $\theta$ is equal to :

• A. ${90}^o$
• B. ${60}^o$
• C. ${45}^o$
• D. ${30}^o$

Answer 1

The correct option is B ${60}^o$

$\angle AOT=\angle APM$ (correspondence because PM $\parallel$ OB)
$\theta =\angle APM$
$\angle APM=\angle C\times M$ (correspondence OA $\parallel$ TC$)
$\angle C\times M=\angle CTB$ (correspondence XM $\parallel$ TB$)
$\theta =\angle CTB$
$\angle APM=\angle OPT$ (Law of Reflection )
$\theta =\angle OPT$
$\angle CTB=\angle PTO$
$\theta =\angle PTO$
In $△OTP$
$\theta +\theta +\theta =180$
$3\theta =180$
$\theta ={60}^o$