Question

A beaker of height '3h' has a radius 'h'. A thin rod of height 'h' is placed to the wall of the beaker. A person can see the top end of the rod from the opposite edge of the beaker through a pin hole. When the beaker is filled with a liquid up to a height '2h', the person can see the bottom end of the rod. The refractive index of the liquid is :

• A. $\frac{3}{2}$
• B. $\frac{\sqrt{3}}{2}$
• C. $\frac{5}{2}$
• D. $\sqrt{\frac{5}{2}}$

Answer 1

Answer: (D)

$\sqrt{\frac{5}{2}}$

The refractive index of a medium is given by,

$\mu =\frac{sini}{sinr}$

Now, from the data given,

sin i = $\frac{h}{\sqrt{h^2+h^2}}$

Similarly, sin r = $\frac{h}{\sqrt{h^2+{2h}^2}}$

Hence, $\mu =\frac{\sqrt{5}}{2}$