There are certain materials developed in laboratories which have a negative refractive index. $A$ ray incident from air (medium $1$) into such a medium (medium $2$) shall follow a path given by

$A$ wave has velocity $u$ in medium $P$ and velocity $2u$ in medium $Q.$ If the wave is incident in medium $P$ at an angle of $30^\circ,$ then the angle of refraction will be .... $^o$

The velocity of light in glass having a refractive index of $1.5$ is $2 \times 10^8 \ m/s$. What is the refractive index of a liquid in which the velocity of light is $2.50 \times 10^8 \ m/s$?

The $X-Y$ plane is taken as the boundary between two transparent media $M_{1}$ and $M_{2}$. $M_{1}$ in $Z \geq 0$ has a refractive index of $\sqrt{2}$ and $M_{2}$ with $Z < 0$ has a refractive index of $\sqrt{3}$. $A$ ray of light travelling in $M_{1}$ along the direction given by the vector $\overrightarrow{A} = 4\sqrt{3}\hat{i} - 3\sqrt{3}\hat{j} - 5\hat{k}$ is incident on the plane of separation. The value of the difference between the angle of incidence in $M_{1}$ and the angle of refraction in $M_{2}$ will be $....$ degrees.

Monochromatic light of frequency $5 \times 10^{14} \ Hz$ travelling in vacuum enters a medium of refractive index $1.5$. Its wavelength in the medium is ....... $\mathring{A}$.

$A$ glass cube of length $24 \ cm$ has a small air bubble trapped inside. When viewed normally from one face,it is $10 \ cm$ below the surface. When viewed normally from the opposite face,its apparent distance is $6 \ cm$. The refractive index of glass is: