question_answer

Two mirrors, placed perpendicularly form two sides of a vessel filled with water. A light ray is incident on the water surface at an angle\[\alpha \]and emerges at an angle\[\beta \]after getting reflected from both the mirrors inside. The relation between\[\alpha \]and\[\beta \]is expressed as

A)  \[\alpha =\beta \]

B)  \[\alpha >\beta \]

C)  \[\alpha <\beta \]

D)  All are possible depending upon\[\alpha \]

Correct Answer: A

Solution :

From above diagram, we have \[90-{{\theta }_{1}}+90-\theta +45{}^\circ +90+{{\theta }_{2}}=180{}^\circ \] \[\Rightarrow \]\[{{\theta }_{1}}+\theta =45{}^\circ ={{\theta }_{1}}+{{\theta }_{2}}\] \[\Rightarrow \]\[{{\theta }_{1}}={{\theta }_{2}}\] \[\Rightarrow \]\[\alpha =\beta \]