$A$ 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:

$A$ 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 $4/3$)

$A$ ray of light falls on a transparent glass slab with a refractive index (relative to air) of $1.62$. The angle of incidence for which the reflected and refracted rays are mutually perpendicular 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 $m/s$.

From the figure shown,establish a relation between $\mu_1, \mu_2, \mu_3$.

$A$ light ray is incident on a medium of refractive index $\mu$. The angle of incidence is twice the angle of refraction. The angle of incidence is: