The refractive index of a medium is $\frac{3}{2}$. The speed of light in this medium is . . . . . . $ms^{-1}$. (Speed of light in vacuum is $c = 3 \times 10^{8} \,ms^{-1}$)

$A$ light ray undergoes refraction from air to water,water to glass,and finally from glass back to air. If the emergent ray is parallel to the incident ray,which of the following relations is correct? ($n_{a}, n_{w}, n_{g}$ represent the refractive indices of air,water,and glass respectively.)

Let the $x-z$ plane be the boundary between two transparent media. Medium $1$ in $z \ge 0$ has a refractive index of $\sqrt{2}$ and medium $2$ with $z < 0$ has a refractive index of $\sqrt{3}$. $A$ ray of light in medium $1$ given by the vector $\overrightarrow{A} = 6\sqrt{3} \widehat{i} + 8\sqrt{3} \widehat{j} - 10\widehat{k}$ is incident on the plane of separation. The angle of refraction in medium $2$ is ......$^o$.

Frosted glass is widely used for translucent windows. The region where a transparent adhesive tape is stuck over the frosted glass becomes transparent. The most reasonable explanation for this is:

The refractive index of air with respect to vacuum is . . . . . . .

The refractive indices of glass and water with respect to air are $3/2$ and $4/3$ respectively. The refractive index of glass with respect to water is: