The velocity of light in a medium is $1.5 \times 10^8 \ m/s$. Its refractive index will be:

$A$ 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:

$A$ beam of light has a small wavelength spread $\delta \lambda$ about a central wavelength $\lambda$. The beam travels in vacuum until it enters a glass plate at an angle $\theta$ relative to the normal to the plate,as shown in the figure. The index of refraction of the glass is given by $n(\lambda)$. The angular spread $\delta \theta'$ of the refracted beam is given by

When a light ray enters from medium $i$ to medium $j$,if $_i\mu_j$ represents the refractive index,what is the product of $_2\mu_1 \times _3\mu_2 \times _4\mu_3$?

The optical properties of a medium are governed by the relative permittivity $(\epsilon_r)$ and relative permeability $(\mu_r)$. The refractive index is defined as $n = \sqrt{\epsilon_r \mu_r}$. For ordinary material $\epsilon_r > 0$ and $\mu_r > 0$ and the positive sign is taken for the square root. In $1964$,a Russian scientist $V$. Veselago postulated the existence of material with $\epsilon_r < 0$ and $\mu_r < 0$. Since then,such 'metamaterials' have been produced in the laboratories and their optical properties studied. For such materials $n = -\sqrt{\epsilon_r \mu_r}$. As light enters a medium of such refractive index,the phases travel away from the direction of propagation.
$(i)$ According to the description above,show that if rays of light enter such a medium from air (refractive index $= 1$) at an angle $\theta_i$ in the $2^{nd}$ quadrant,then the refracted beam is in the $3^{rd}$ quadrant.
$(ii)$ Prove that Snell's law holds for such a medium.

$A$ monochromatic light of frequency $5 \times 10^{14} \ Hz$ travelling through air is incident on a medium of refractive index $2$. What will be the wavelength of the refracted light (in $nm$)?