$A$ light wave travels through three transparent materials of equal thickness. Rank in order,from the highest to lowest,the indices of refraction $n_1, n_2$ and $n_3$.

$A$ circular disc of radius $R$ is placed co-axially and horizontally inside an opaque hemispherical bowl of radius $a$ (See figure). The far edge of the disc is just visible when viewed from the edge of the bowl. The bowl is filled with a transparent liquid of refractive index $\mu$ and the near edge of the disc becomes just visible. How far below the top of the bowl is the disc placed?

$A$ monochromatic light of frequency $5 \times 10^{14} \ Hz$ travelling through air is incident on a medium of refractive index $2$. What will be the wavelength of the refracted light (in $nm$)?

Give one example of a substance whose mass density is low but optical density is high.

$A$ tank is filled with water to a height of $12.5 \;cm$. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be $9.4 \;cm$. What is the refractive index of water?
If water is replaced by a liquid of refractive index $1.63$ up to the same height,by what distance would the microscope have to be moved to focus on the needle again?

The speed of light in air is $3 \times 10^8 \, m/s$. What will be its speed in diamond,whose refractive index is $2.4$?