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 $\mu_r = 1$)

Captain Jack Sparrow tries to observe a fish almost vertically below him in a magical sea of variable refractive index $\mu = y^2 + 1$,where $y$ is the depth below the water surface. Find the apparent depth of the fish below the water level as seen by Captain Jack Sparrow. The actual depth of the fish is $1 \ m$.

The optical path of a monochromatic light is the same if it goes through $4.0 \, cm$ of glass or $4.5 \, cm$ of water. If the refractive index of glass is $1.53$,the refractive index of water is:

If $n_{21} > 1$,then write the relation between the angle of incidence and the angle of refraction.

When a light ray enters a medium with refractive index $\mu$,it is observed that the angle of refraction is half the angle of incidence. The angle of incidence is .........

An electromagnetic wave of wavelength $\lambda_0$ (in vacuum) passes from $P$ towards $Q$ crossing three different media of refractive index $\mu, 2\mu$ and $3\mu$ respectively as shown in the figure. Let $\phi_P$ and $\phi_Q$ be the phase of the wave at points $P$ and $Q$. Find the phase difference $\phi_Q - \phi_P$. [Take: $\mu = 1$]