$A$ light ray enters a solid glass sphere of refractive index $\mu=\sqrt{3}$ at an angle of incidence $60^{\circ}$. The ray is both reflected and refracted at the farther surface of the sphere. The angle (in degrees) between the reflected and refracted rays at this surface is......

The refractive index of water is $1.33$. The direction in which a man under water should look to see the setting sun is

$A$ light of wavelength $\lambda_{1}$ and velocity $C_{1}$ travels from the first medium of refractive index $\mu_{1}$ into the second medium of refractive index $\mu_{2}$. The wavelength and velocity of light in the second medium are $\lambda_{2}$ and $C_{2}$ respectively. The refractive index of the second medium with respect to the first medium is given by:

Monochromatic light of wavelength $589 \; nm$ is incident from air on a water surface. What are the wavelength,frequency,and speed of
$(a)$ reflected,and
$(b)$ refracted light? Refractive index of water is $1.33$.

The $X-Y$ plane is taken as the boundary between two transparent media $M_{1}$ and $M_{2}$. $M_{1}$ in $Z \geq 0$ has a refractive index of $\sqrt{2}$ and $M_{2}$ with $Z < 0$ has a refractive index of $\sqrt{3}$. $A$ ray of light travelling in $M_{1}$ along the direction given by the vector $\overrightarrow{A} = 4\sqrt{3}\hat{i} - 3\sqrt{3}\hat{j} - 5\hat{k}$ is incident on the plane of separation. The value of the difference between the angle of incidence in $M_{1}$ and the angle of refraction in $M_{2}$ will be $....$ degrees.

The refractive index of water is $1.33$. What will be the speed of light in water?