$A$ light ray is incident from a medium of refractive index $2$ into a medium of refractive index $\sqrt{3}$. The critical angle is (in $^{\circ}$)

What should be the maximum acceptance angle at the air-core interface of an optical fibre if $n_1$ and $n_2$ are the refractive indices of the core and the cladding,respectively?

$A$ point source of light is kept below the surface of water $(n_{w} = 4/3)$ at a depth of $\sqrt{7} \ m$. The radius of the circular bright patch of light noticed on the surface of water is

$A$ 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 . . . . . . .

Light travels in two media $A$ and $B$ with speeds $1.8 \times 10^8 \ m/s$ and $2.4 \times 10^8 \ m/s$ respectively. Then the critical angle between them is

On the hypotenuse of a right-angled prism $(30^{\circ}-60^{\circ}-90^{\circ})$ with a refractive index of $1.50$,a drop of liquid is placed as shown in the figure. Light is allowed to fall normally on the short face of the prism. In order for the ray of light to undergo total internal reflection at the hypotenuse,what is the maximum value of the refractive index of the liquid?