A hemispherical vessel is completely filled with a liquid of refractive index $\mu$. A small coin is

Question

A hemispherical vessel is completely filled with a liquid of refractive index $\mu$. A small coin is kept at the lowest point $(O)$ of the vessel as shown in figure. The minimum value of the refractive index of the liquid so that a person can see the coin from point $E$ (at tha level of the vessel) is _____.

Professor PC Thomas Classes · Answer

(c) : For least value of $\mu, i_{c}$ should be maximum.\ Thus, critical angle $i_{c}=45^{\circ}$\ We know that,\ Refractive index, $\mu=\frac{1}{\sin i_{c}}$\ or $\mu=\frac{1}{\frac{1}{\sqrt{2}}}=\sqrt{2}$\