question_answer

The value of \[\theta \] so that the ray retraces the path after it strikes the mirror in water as shown in the diagram is \[({{\mu }_{of\,water}}=4/3)\]

A) \[\theta ={{\sin }^{-1}}\left( \frac{3}{8} \right)\]

B) \[\theta ={{\sin }^{-1}}\left( \frac{1}{2} \right)\]

C) \[\theta ={{\sin }^{-1}}\left( \frac{1}{3} \right)\]            

D) \[\theta ={{\sin }^{-1}}\left( \frac{1}{\sqrt{12}} \right)\]

Correct Answer: A

Solution :

[a]             \[\frac{1}{2}\times 1=\frac{4}{3}\sin \theta \]             \[\theta ={{\sin }^{-1}}\left( \frac{3}{8} \right)\]