JEE Main & Advanced
Sample Paper
JEE Main Sample Paper-47
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 \[\alpha ={{\theta }_{2}}+\theta \] \[\Rightarrow \] \[{{\theta }_{1}}={{\theta }_{2}}\] \[\Rightarrow \] \[\alpha =\beta \]