Question

The refractive index of the water with respect to air is 4/3. What is the refractive index of air with respect to water?

Answer 1

The refractive index is the unit less and the dimensionless quantity. The refractive index is the ratio of the speed of light in air and the speed of light in the medium.

Complete step-by-step answer :
The refractive index of the material is the fraction of the speed of light in air and the speed of light in that medium.
The refractive index is given as:
$\Rightarrow R.I.=\dfrac{c}{v}$

Where, c is the speed of light in air and v is the speed of light in medium.

The refractive index is also given as the ratio of refractive index of the medium and refractive index of the air.
The refractive index of the air is 1.

Given:
The refractive index of the water with respect to air is 4/3

Refractive index of water with respect to air is ${R}_{1} = \dfrac{4}{3}$
The refractive index of the air with respect to water is, ${R}_{w}=\dfrac{1}{{R}_{1}}$
$\begin{aligned} & \Rightarrow {{R}_{w}}=\dfrac{1}{{{R}_{1}}} \\\ & \Rightarrow {{R}_{w}}=\dfrac{1}{{}^{4}/{}_{3}} \\\ & \Rightarrow {{R}_{w}}=\dfrac{3}{4} \\\ \end{aligned}$

Note :The refractive index of water with respect to air is also given as:
$\begin{aligned} & \Rightarrow {{R}_{1}}=\dfrac{{{R}_{w}}}{{{R}_{a}}} \\\ & \Rightarrow {{R}_{1}}=\dfrac{{{R}_{w}}}{1} \\\ & \Rightarrow {{R}_{1}}={{R}_{w}} \\\ \end{aligned}$