question_answer

Two mirror are bended on each other in such a manner that the incident ray on first mirror, parallel to the second mirror, becomes parallel to first mirror by reflection through second mirror, then the angle between the two mirrors is

A)  \[30{}^\circ \]              

B)  \[45{}^\circ \]

C)  \[60{}^\circ \]              

D)  \[75{}^\circ \]

Correct Answer: C

Solution :

 Suppose angle between the both mirrors is\[\theta \] Ray PQ parallel to\[{{M}_{1}}\]and ray RS parallel to \[{{M}_{2}}\] \[\angle {{M}_{1}}S=\angle ORQ=\angle {{M}_{1}}O{{M}_{2}}=\theta \] Similarly \[\angle {{M}_{2}}QP=\angle OQR=\angle {{M}_{2}}O{{M}_{1}}=\theta \] In\[\Delta OPQ\] \[3\theta =180{}^\circ \] \[\theta =60{}^\circ \]