$A$ ray of light travels from air to water to glass and again from glass to air. The refractive index of water with respect to air is '$X$', glass with respect to water is '$Y$', and air with respect to glass is '$Z$'. Which one of the following is correct?

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

Draw a figure that illustrates the reflection and refraction of light.

$A$ ray of light of frequency $5 \times 10^{14} \,Hz$ is passed through a liquid. The wavelength of light measured inside the liquid is found to be $450 \times 10^{-9} \,m$. Calculate the refractive index of the liquid.

The refractive index of the material of a crystal is $1.68$ and that of castor oil is $1.2$. When a ray of light passes from oil to the crystal,its velocity will change by a factor of: