question_answer

A man in an empty swimming pool has a telescope focused at 4'O clock sun. When the swimming pool is filled with water, the man (now inside the water with his telescope undisturbed) observes the setting sun. Find the refractive index of water, if sun rises and sets at 6'O clock.

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

B) \[\frac{2}{\sqrt{3}}\]

C) \[\frac{8}{5}\]

D) \[\frac{2}{5}\]

Correct Answer: B

Solution :

[b] When no water is there in the swimming pool, the telescope is along the line PO. When   water has been filled into the pool, the person is able to see the setting sun, i.e., refracted ray will be along OP while incident ray is along RP, as shown in figure. That is from the object (sun) to the telescope.

Let \[\mu \] be refractive index of water, then

\[\frac{\sin \,{{90}^{o}}}{\sin \,{{60}^{o}}}=\frac{\mu }{1}\]\[\Rightarrow \] \[\mu =\frac{1}{\sin \,{{60}^{o}}}=\frac{2}{\sqrt{3}}\]