For total internal reflection to take place,the angle of incidence $i$ and the refractive index $\mu$ of the medium must satisfy the inequality

$A$ 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 the figure. The minimum value of the refractive index of the liquid so that a person can see the coin from point $E$ (at the level of the vessel) is . . . . . . .

Calculate the critical angle for a glass-air surface,if a ray of light incident in air on the glass surface is deviated by $15^{\circ}$ when the angle of incidence is $45^{\circ}$. (in $^{\circ}$)

$A$ parallel beam of light is incident on a glass prism in the shape of a quarter cylinder of radius $R=0.05 \ m$ and refractive index $n=1.5$,placed on a horizontal table as shown in the figure. Beyond the cylinder,a patch of light is found whose nearest distance $x$ from the cylinder is

$A$ light ray falls on a rectangular glass slab as shown in the figure. If total internal reflection occurs at the vertical face of the slab at point $B$,the refractive index of glass is

$A$ spider and a fly are on opposite sides of the surface of a glass sphere. What is the maximum solid angle $\Omega$ within which the fly can be seen by the spider?
Given: The dimensions of the spider and the fly are very small with respect to the sphere. The refractive index of the glass is $\mu_g = \sqrt{2}$.