In a medium,the speed of a light wave decreases to $0.2$ times its speed in free space. The ratio of relative permittivity to the refractive index of the medium is $x: 1$. The value of $x$ is $...........$ (Given: speed of light in free space $= 3 \times 10^8 \ m \ s^{-1}$ and for the given medium $\mu_r = 1$)

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

Light travels through water in a beaker. The height of the water column is $h$. If the refractive index of water is $\mu_{w}$ and $C$ is the velocity of light in air,the time taken by light to travel through the water will be:

In the formation of a primary rainbow,the sunlight rays emerge at minimum deviation from a raindrop after:

The refractive index of the material of a crystal is $1.68$ and that of castor oil is $1.2$. When a ray of light passes from oil to the crystal,its velocity will change by a factor of:

The angles of incidence and refraction of a monochromatic ray of light of wavelength $\lambda$ at an air-glass interface are $i$ and $r$,respectively. $A$ parallel beam of light with a small spread $\delta \lambda$ in wavelength about a mean wavelength $\lambda$ is refracted at the same air-glass interface. The refractive index $\mu$ of glass depends on the wavelength $\lambda$ as $\mu(\lambda)=a+b / \lambda^2$,where $a$ and $b$ are constants. Then,the angular spread in the angle of refraction of the beam is