Question

Refractive index of glass with respect to water is $\left( {9/8} \right)$. Refractive index of glass with respect to air is $\left( {3/2} \right)$. Find the refractive index of water with respect to air.

Answer 1

- Hint: The refractive index n of an optical medium is defined as the ratio of the speed of light in vacuum, and the phase velocity v of light in the medium, $n = \dfrac{c}{v}$.
Formula used: The refractive index of glass with respect to water is given as ${R_{gw}} = \dfrac{{{R_g}}}{{{R_w}}}$, The refractive index of glass with respect to air ${R_{ga}} = \dfrac{{{R_g}}}{{{R_a}}}$and refractive index of water with respect to air ${R_{wa}} = \dfrac{{{R_w}}}{{{R_a}}}$.

Complete step-by-step solution -

According to the question we have to find the refractive index of water with respect to air.
The refractive index of glass is ${R_g}$, the refractive index of air is ${R_a}$ and the refractive index of water is ${R_w}$.
The refractive index of glass with respect to water is given as,
$
  {R_{gw}} = \dfrac{{{R_g}}}{{{R_w}}} \\
  \dfrac{9}{8} = \dfrac{{{R_g}}}{{{R_w}}}.........(1) \\
$
The refractive index of glass with respect to air is given as,
$
  {R_{ga}} = \dfrac{{{R_g}}}{{{R_a}}} \\
  \dfrac{3}{2} = \dfrac{{{R_g}}}{{{R_a}}}........\left( 2 \right) \\
 $
The refractive index of water with respect to air is given as,
${R_{wa}} = \dfrac{{{R_w}}}{{{R_a}}}.........\left( 3 \right)$
Substitute the values from equation $\left( 1 \right)$ and $\left( 2 \right)$ in equation $\left( 3 \right)$, we get
${R_{wa}} = \dfrac{4}{3}$.
Thus, the refractive index of water with respect to air is $\dfrac{4}{3}$

Note: In such types of question where we have to find the refractive index of water with respect to air there we will apply the concept of refractive index and follow various steps i.e. first write what is given then find the refractive index of glass with respect to water , the refractive index of glass with respect to air , the refractive index of water with respect to air. After that, substitute the value of refractive index of glass with respect to water and refractive index of glass with respect to air in refractive index of water with respect to air to get an answer.