If the angle of incidence is twice the angle of refraction in a medium of refractive index $\mu$,then the angle of incidence is

$A$ light ray passes through four transparent media with refractive indices $\mu_1, \mu_2, \mu_3$ and $\mu_4$ as shown in the figure. All surfaces are parallel to each other. If the emergent ray $CD$ is parallel to the incident ray $AB$,then:

The absolute refractive indices of glass and water are $\frac{3}{2}$ and $\frac{4}{3}$,respectively. The ratio of the velocity of light in glass to that in water will be:

If the ray $CD$ is parallel to the ray $AB$,then:

An infinitely long cylinder of radius $R$ is made of an unusual exotic material with refractive index $-1$ (See figure). The cylinder is placed between two planes whose normals are along the $y$-direction. The center of the cylinder $O$ lies along the $y$-axis. $A$ narrow laser beam is directed along the $y$-direction from the lower plate. The laser source is at a horizontal distance $x$ from the diameter in the $y$-direction. Find the range of $x$ such that light emitted from the lower plane does not reach the upper plane.

$A$ mixture of a pure liquid and a solution in a long vertical column (i.e., horizontal dimensions << vertical dimensions) produces diffusion of solute particles and hence a refractive index gradient along the vertical dimension. $A$ ray of light entering the column at right angles to the vertical is deviated from its original path. Find the deviation in travelling a horizontal distance $d << h$, where $h$ is the height of the column.