$A$ 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 $4/3$)

An electromagnetic wave,whose wave normal makes an angle of $45^{\circ}$ with the vertical,travelling in air strikes a horizontal liquid surface. While travelling through the liquid it gets deviated through $15^{\circ}$. What is the speed of the electromagnetic wave in the liquid,if the speed of electromagnetic wave in air is $3 \times 10^8 \ m/s$? $(\sin 30^{\circ} = 0.5, \sin 45^{\circ} = \frac{1}{\sqrt{2}})$

The refractive index of water and glass with respect to air is $1.3$ and $1.5$ respectively. Then the refractive index of glass with respect to water is

$A$ fish rising vertically at the rate of $3 \, m/s$ to the surface of water observes a bird above the water,diving vertically towards it at the rate of $9 \, m/s$. The refractive index of water is $4/3$. Calculate the actual velocity (velocity $w.r.t$ ground) of the bird in $m/s$.

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.

Write two definitions and equations of relative refractive index.