Question

Refractive index of glass is 1.6 and that of diamond 2.4. Find the refractive index of glass with respect to diamond and diamond with respect to that of glass

Answer 1

Step 1: Given that:

Refractive index of glass(${\mu }_g$) = $1.6$

Refractive index of diamond(${\mu }_d$) = $2.4$

Step 2: Formula used:

The Refractive index of one medium with respect to other is the ratio of the refractive index of one medium to the refractive index of other media with respect to air.

That is if ${\mu }_1$ be the refractive index of medium 1 and ${\mu }_2$ be the refractive index of medium 2 then,

The refractive index of medium 1 with respect to medium 2 (${}^2{\mu }_1$) = $\frac{{\mu }_1}{{\mu }_2}$

And,

Refractive index of medium 2 with respect to medium 1 is the reciprocal of the refractive index of medium 1 with respect to medium 2.

That is ${}^1{\mu }_2=\frac{1}{{}^2{\mu }_1}$

Step 3: Calculation of the refractive index of glass with respect to diamond:

${}^d{\mu }_g=\frac{{\mu }_g}{{\mu }_d}$

${}^d{\mu }_g=\frac{1.6}{2.4}$

${}^d{\mu }_g=\frac{2}{3}$

Step 4: Calculation of the refractive index of diamond with respect to glass:

${}^g{\mu }_d=\frac{1}{{}^d{\mu }_g}$

${}^g{\mu }_d=\frac{1}{\frac{2}{3}}$

${}^g{\mu }_d=\frac{3}{2}$

${}^g{\mu }_d=1.5$

Thus,

The refractive index of glass with respect to diamond= $\frac{2}{3}=0.67$

The refractive index of diamond with respect to glass= $1.5$