When light travels from glass to air,the incident angle is ${\theta _1}$ and the refracted angle is ${\theta _2}$. The true relation is:

$A$ ray of light is incident at the glass-water interface at an angle $i$. It emerges finally parallel to the surface of water. If the refractive index of water is $\mu_w = 4/3$,then the value of the refractive index of glass $\mu_g$ is:

$A$ small coin is fixed at the centre of the base of an empty cylindrical steel container having radius $R=1 \,m$ and height $d=4 \,m$. At time $t=0$,the container starts getting filled with water at a flow rate of $Q=0.1 \,m^3/s$ without disturbing the coin. Find the approximate time $t$ in seconds when the coin will first be seen by the observer $O$ from a height of $H=5.75 \,m$ above and $L=1.5 \,m$ radially away from the coin as shown in the figure. (Take refractive index of water,$n=1.33$ or $4/3$)

Let the $x-z$ plane be the boundary between two transparent media. Medium $1$ in $z \ge 0$ has a refractive index of $\sqrt{2}$ and medium $2$ with $z < 0$ has a refractive index of $\sqrt{3}$. $A$ ray of light in medium $1$ given by the vector $\overrightarrow{A} = 6\sqrt{3} \widehat{i} + 8\sqrt{3} \widehat{j} - 10\widehat{k}$ is incident on the plane of separation. The angle of refraction in medium $2$ is ......$^o$.

If the wavelength of light in air is $4200\, \mathring A$,what will be the wavelength of light in water $(\mu = 4/3)$ in $\mathring A$?

Blue light travelling in a vacuum has a wavelength of $450 \ nm$. It enters a medium whose refractive index is $1.5$. What is its frequency in the medium? $(Speed of light in vacuum = 3 \times 10^8 \ m \ s^{-1})$