question_answer

A diver, at a depth of 12 metre from the surface of the water, sees the sky with in a cone whose half vertex angle \[\left( _{a}{{\mu }_{\omega =}}\frac{4}{3} \right)\]is :

A) \[\cos -\frac{4}{3}\]                                       

B) \[{{\sin }^{-1}}\frac{4}{3}\]

C) \[{{90}^{0}}\]                                    

D) \[{{\sin }^{-1}}\frac{3}{4}\]

Correct Answer: D

Solution :

Let diver is placed at S. He will see a cone of maximum radius r. In this condition                 \[\sin {{i}_{C}}=\frac{1}{_{a}{{\mu }_{\omega }}}\] \[\Rightarrow \]               \[\sin {{i}_{c}}=\frac{1}{4/3}\] \[\Rightarrow \]               \[\sin {{i}_{c}}=\frac{3}{4}\] Therefore,    \[{{i}_{c}}={{\sin }^{-1}}\left( \frac{3}{4} \right)\]