The absolute refractive indices of glass and water are $\frac{3}{2}$ and $\frac{4}{3}$respectively. If the speed of light in the glass is $2\times {10}^8\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$, calculate the speed of light in

a. vacuum.

Step 1 - Given data

Refractive index of glass, ${\mu }_g=\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$

Speed of light in the glass, $v_g=2\times {10}^8\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

Step 2 - Finding the speed of light in vacuum.

Assume the speed of light in a vacuum as $c$.

The absolute refractive index of glass in terms of speed of light is given by,

${\mu }_g=\frac{c}{v_g}$.

Substitute the values into the formula.

$$\begin{gathered} \frac{3}{2}=\frac{c}{2\times {10}^8{\displaystyle \raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.}} \\ c=\frac{3\times 2\times {10}^8}{2} \\ =3\times {10}^8\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right. \end{gathered}$$

The speed of light in a vacuum is $3\times {10}^8\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$.