Electromagnetic radiation of frequency $n$,wavelength $\lambda$,travelling with velocity $v$ in air,enters a glass slab of refractive index $\mu$. The frequency,wavelength,and velocity of light in the glass slab will be respectively:

$A$ ray of light of frequency $5 \times 10^{14} \,Hz$ is passed through a liquid. The wavelength of light measured inside the liquid is found to be $450 \times 10^{-9} \,m$. Calculate the refractive index of the liquid.

$A$ tank is filled with water to a height of $12.5 \, cm$. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be $9.4 \, cm$. If water is replaced by a liquid of refractive index $1.63$ up to the same height,what will be the apparent depth of the needle in $cm$?

$A$ 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 $\mu = 4/3$).

$A$ light ray of frequency '$v$' and wavelength '$\lambda$' enters a liquid of refractive index $\frac{3}{2}$. The ray travels in the liquid with:

$A$ mixture of a pure liquid and a solution in a long vertical column (i.e., horizontal dimensions << vertical dimensions) produces diffusion of solute particles and hence a refractive index gradient along the vertical dimension. $A$ ray of light entering the column at right angles to the vertical is deviated from its original path. Find the deviation in travelling a horizontal distance $d << h$, where $h$ is the height of the column.