The frequency of a light wave in a material is $2 \times 10^{14} \ Hz$ and its wavelength is $5000 \ \mathring{A}$. The refractive index of the material will be:

An observer can see the top of a thin rod of height $h$ through a pinhole. The height of the container is $3h$ and its radius is $2h$. When the container is filled with a liquid up to a height of $2h$,the observer can see the bottom end of the rod. Find the refractive index of the liquid.

$A$ ray of light falls on a transparent glass slab with a refractive index (relative to air) of $1.62$. The angle of incidence for which the reflected and refracted rays are mutually perpendicular is

$A$ ray of light is incident on a transparent sphere at an angle of $\pi / 4$ and is refracted at an angle $r$. The ray emerges from the sphere after suffering one internal reflection. The total angle of deviation of the ray is

The optical path of a monochromatic light is the same if it goes through $4.0 \, cm$ of glass or $4.5 \, cm$ of water. If the refractive index of glass is $1.53$,the refractive index of water is:

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.