question_answer

An observer can see through a pin?hole the top end of a thin rod of height h, placed as shown in the figure.  The beaker height is 3h and its radius h.  When the beaker is filled with a liquid up to a height 2h, he can see the lower end of the rod.  Then the refractive index of the liquid is  [IIT-JEE (Screening) 2002]

A)            5/2                                           

B)            \[\sqrt{(5/2)}\]

C)            \[\sqrt{(3/2)}\]                   

D)            3/2

Correct Answer: B

Solution :

                   The line of sight of the observer remains constant, making an angle of 45° with the normal. \[\sin \theta =\frac{h}{\sqrt{{{h}^{2}}+{{(2h)}^{2}}}}\]=\[\frac{1}{\sqrt{5}}\]                    \[\mu =\frac{\sin {{45}^{o}}}{\sin \theta }\]            \[=\frac{1/\sqrt{2}}{1/\sqrt{5}}=\sqrt{\left( \frac{5}{2} \right)}\]