Question

An observer can see through a pin-hole at the top end of a thin rod of 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:

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

Answer 1

The correct option is A $\frac{5}{2\sqrt{2}}$

${\mu }_N^2=\frac{\sin i}{\sin r}=\frac{\frac{2}{5}}{\frac{1}{\sqrt{2}}}=\frac{2}{5}\times \frac{\sqrt{2}}{1}{\mu }_a^{\omega }=\frac{5}{2\sqrt{2}}$