question_answer

Two plane mirrors AB and CD are placed at right angles to one another. A ray of light PQ hits AB at Q making an angle of \[\text{45 }\!\!{}^\circ\!\!\text{ }\] as shown in the diagram. This ray will be reflected from mirror CD at an angle.

A) \[\text{20 }\!\!{}^\circ\!\!\text{ }\]                      

B) \[\text{35 }\!\!{}^\circ\!\!\text{ }\]          

C) \[\text{45 }\!\!{}^\circ\!\!\text{ }\]                      

D) \[\text{60 }\!\!{}^\circ\!\!\text{ }\]

Correct Answer: C

Solution :

Since OS is normal to the mirror AB. \[\therefore \angle {{i}_{1}}=45{}^\circ ,\] Also \[\angle {{r}_{1}}=45{}^\circ \] In \[\Delta CQR,\angle C=90{}^\circ ,\angle CQR=45{}^\circ \therefore \angle CRQ=45{}^\circ \] [\[\because \]Sum of all the three angles in triangle is\[\text{180 }\!\!{}^\circ\!\!\text{ }\].] Hence, \[\angle {{\text{i}}_{2}}=45{}^\circ \] [TR is the normal to the mirror BD] \[\therefore \angle {{r}_{2}}=45{}^\circ \]