The apparent depth of water in a cylindrical water tank of diameter $2R \ cm$ is reducing at the rate of $x \ cm/minute$ when water is being drained out at a constant rate. The amount of water drained in $c.c./minute$ is: ($n_1 =$ refractive index of air,$n_2 =$ refractive index of water)

$A$ 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:

The speed of light in a medium is $200 \times 10^8 \text{ cm/s}$. The refractive index of the medium is . . . . . . $(c = 3 \times 10^8 \text{ m/s})$.

The refractive index of glass is $1.6$ and the speed of light in glass will be . . . . . . . Speed of light in vacuum is $3 \times 10^{8} \,m \,s^{-1}$.

$A$ fish rising vertically up towards the surface of water with speed $3 \; ms^{-1}$ observes a bird diving vertically down towards it with speed $9 \; ms^{-1}$. The actual velocity of the bird is.......$ms^{-1}$ (Assume refractive index of water $\mu = 4/3$).

$A$ monochromatic light is travelling in a medium of refractive index $n=1.6$. It enters a stack of glass layers from the bottom side at an angle $\theta=30^{\circ}$. The interfaces of the glass layers are parallel to each other. The refractive indices of different glass layers are monotonically decreasing as $n_m=n-m \Delta n$,where $n_m$ is the refractive index of the $m^{\text{th}}$ slab and $\Delta n=0.1$ (see the figure). The ray is refracted out parallel to the interface between the $(m-1)^{\text{th}}$ and $m^{\text{th}}$ slabs from the right side of the stack. What is the value of $m$?