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

Let refractive index of glass is $R_g$, refractive index of air is $R_a$ and refractive index of water is $R_w$.

The refractive index of glass with respect to water is given as,

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

$\frac{9}{8}=\frac{R_g}{R_w}$ (1)

The refractive index of glass with respect to air is given as,

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

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

The refractive index of water with respect to air is given as,

$R_{wa}=\frac{R_w}{R_a}$ (3)

Substitute the values from equation (1) and (2) in equation (3), we get

$R_{wa}=\frac{4}{3}$

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