question_answer

A man is standing at the edge of a 1 m deep swimming pool, completely filled with a liquid of refractive index \[\sqrt{3/2}\]. The eyes of the man are \[\sqrt{3}m\] above the ground. A coin located at the bottom of the pool appears to be at an angle of depression of \[\text{3}0{}^\circ \] with reference to the eye of man. Then horizontal distance (represented by \[\times \] in the figure) of the coin from the eye of the man is .....   mm.

A) 2000

B) 3000             

C) 4000

D) 8000

Correct Answer: C

Solution :

[c]

\[\sin 60{}^\circ =\sqrt{\frac{3}{2}}\,\,\sin r\,\,\,\,\,\Rightarrow \,\,\,\,r=45{}^\circ \]

\[\therefore \]    S = h = 1 m

\[y=H\tan \,\,60{}^\circ =3\,m\]

\[\therefore \]    \[x=S+y=4\,m=4000\text{ }mm\]