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 :

  By analysis the diagram and with the help of laws of reflection and refraction. \[\alpha +90-{{\theta }_{1}}+90-\theta \] \[=90-\alpha +90+{{\theta }_{2}}+\theta ={{180}^{o}}\] \[\Rightarrow \]            \[\alpha -{{\theta }_{1}}-\theta -\alpha +{{\theta }_{2}}+\theta =0\] and      \[\alpha ={{\theta }_{2}}+\theta \] \[\Rightarrow \]            \[{{\theta }_{1}}={{\theta }_{2}}\] \[\Rightarrow \]            \[\alpha =\beta \]