question_answer

What should be the angle between the two mirrors so that, whatever may be the angle of incidence, the incident ray and the reflected ray from the two mirrors will he parallel to each other?

A) \[45{}^\circ \]

B)        \[75{}^\circ \]

C) \[90{}^\circ \]  

D)        \[120{}^\circ \]

Correct Answer: C

Solution :

               Let the angle between total deviation for the ray mirrors be\[\theta \], then For the resultant ray to be parallel, \[\delta \] should be\[{{180}^{o}}\] \[\therefore \]  \[360-2({{i}_{1}}+{{i}_{2}})={{180}^{o}}\] \[\Rightarrow \]                           \[({{i}_{1}}+{{i}_{2}})={{90}^{o}}\] From the geometry of figure,                 \[90-{{i}_{1}}+90-{{i}_{2}}+\theta =180\] \[\therefore \]  \[{{i}_{1}}+{{i}_{2}}=\theta \] Hence, angle between the mirror should be\[{{90}^{o}}\].