Question

The Refractive index of glass with respect to water is (9/8) . The Refractive index of glass with respect to air is (3/2). Find the refractive index of water with respect to air.

Answer 1

Step 1: Given information:

The refractive index of glass with respect to water $R_{gw}$is $\left(\raisebox{1ex}{$9$}\!\left/ \!\raisebox{-1ex}{$8$}\right.\right)$.

The refractive index of glass with respect to air is $R_{ga}$is $\left(\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)$.

To find the refractive index of water with respect to air $R_{wa}$.

Step 2: To find the refractive index of water with respect to air $R_{wa}$.

The refractive index of glass with respect to water is

$R_{gw}=\frac{R_g}{R_w}$

and

$\frac{9}{8}=\frac{R_g}{R_w}$

again the refractive index of glass with respect to air is

$R_{ga}=\frac{R_g}{R_a}$

and

$\frac{3}{2}=\frac{R_g}{R_a}$

So the refractive index of water with respect to air is

$R_{wa}=\frac{R_{ga}}{R_{gw}}=\frac{{\displaystyle \frac{R_g}{R_a}}}{{\displaystyle \frac{R_g}{R_w}}}=\frac{R_w}{R_a}$

$\therefore R_{wa}=\frac{{\displaystyle \frac{3}{2}}}{{\displaystyle \frac{9}{8}}}=\frac{4}{3}$

Hence, the refractive index of water with respect to air is$\frac{4}{3}$.