question_answer

    Two plane mirrors are inclined to each other such that a ray of light incident on the first mirror and parallel to the second is reflected from the second mirror parallel to the first mirror. The angle between the two mirrors is

A)  \[30{}^\circ \]                                  

B)  \[45{}^\circ \]

C)  \[60{}^\circ \]                                  

D)  \[75{}^\circ \]

Correct Answer: C

Solution :

                Let the angle between the two mirrors be\[\theta \]. Ray PQ is parallel to mirror\[{{M}_{1}}\]and RS is parallel to\[{{M}_{2}}\]. So \[\angle {{m}_{1}}RS=\angle ORQ=\angle {{M}_{1}}O{{M}_{2}}=\theta \] Similarly, \[\angle {{M}_{2}}QP=\angle OQR=\angle {{M}_{2}}O{{M}_{1}}=\theta \] \[\therefore \]In \[\Delta ORQ,\text{ }3\theta =180{}^\circ \] \[\theta =60{}^\circ .\]