$A$ beam of monochromatic blue light of wavelength $4200 Å$ in air travels in water of refractive index $4/3$. Its wavelength in water will be: (in $Å$)

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

Let the $x-z$ plane be the boundary between two transparent media. Medium $1$ in $z \ge 0$ has a refractive index of $\sqrt{2}$ and medium $2$ with $z < 0$ has a refractive index of $\sqrt{3}$. $A$ ray of light in medium $1$ given by the vector $\overrightarrow{A} = 6\sqrt{3} \widehat{i} + 8\sqrt{3} \widehat{j} - 10\widehat{k}$ is incident on the plane of separation. The angle of refraction in medium $2$ is ......$^o$.

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:

The refractive index of air is $1.0003$. The thickness of an air column that will contain one more wavelength of yellow light $(6000 \mathring A)$ than in the same thickness in a vacuum is:

Calculate the value of $n_{32} \times n_{21} = .... $