Clarify the meanings of optical density and mass density.

The index of refraction of diamond is $2.0$. The velocity of light in diamond in $cm/s$ is approximately:

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

$A$ light beam is travelling from Region $I$ to Region $IV$ (Refer Figure). The refractive indices in Regions $I$,$II$,$III$,and $IV$ are $n_0$,$\frac{n_0}{2}$,$\frac{n_0}{6}$,and $\frac{n_0}{8}$,respectively. The angle of incidence $\theta$ for which the beam just misses entering Region $IV$ is:

If light passes near a massive object,the gravitational interaction causes a bending of the ray. This can be thought of as happening due to a change in the effective refractive index of the medium given by $n = 1 + \frac{2GM}{rc^2}$,where $r$ is the distance of the point of consideration from the centre of the mass of the massive body,$G$ is the universal gravitational constant,$M$ is the mass of the body,and $c$ is the speed of light in vacuum. Considering a spherical object,find the deviation of the ray from the original path as it grazes the object.

Light travels through a glass plate of thickness $t$ and having refractive index $n$. If $c$ is the velocity of light in vacuum,the time taken by the light to travel this thickness of glass is