Question

A mirror is inclined at an angle $\theta$ with the horizontal. If a ray of light is incident on the mirror at an angle $\theta$, then the reflected ray makes the following angle with the horizontal :

• A. $\theta$
• B. $2\theta$
• C. $\frac{\theta }{2}$
• D. ${90}^{\circ }$

Answer 1

Answer: (D)

${90}^{\circ }$

$OA$ & $OB$ are two mirrors inclined at an angle $\theta$.
$\overrightarrow{PQ}$ is the incident ray
$\overrightarrow{QR}$ is the reflected ray
$XY$ is the normal on $OA$ mirror.
So, $\angle PQX=\theta =\angle XQR$
$QR$ is traced back to meet mirror $OB$ at $S$.
So, $\angle$ $RQA$ $=90-\theta$
$\therefore \angle OQS=90-\theta$
in triangle $\Delta OQS,\theta +{90}^{\circ }-\theta +\angle OSQ={180}^{\circ }$
$\angle OSQ={90}^{\circ }$
So, reflected ray makes an angle ${90}^{\circ }$ with the horizontal.