Question

The absolute refractive index of glass and water are $3/2$ and $4/3$, respectively. If the speed of light in glass is $2\times {10}^8$ m/s, calculate the speed of light in :
(a) vacuum
(b) water

Answer 1

Given : $n_{water}=\frac{4}{3}$ $n_{glass}=\frac{3}{2}$ $v_{glass}=2\times {10}^8$ m/s $n_{air}=1$

Speed of light in a medium $v_{medium}=\frac{c}{n}$

where $c$ and $n$ are the speed of light in vacuum and refractive index of medium respectively.

(a) : $v_{glass}=\frac{c}{n_{glass}}$

$\therefore$ $2\times {10}^8=\frac{c}{\left(3/2\right)}$ $⟹c=3\times {10}^8$ m/s

(b) : $v_{water}=\frac{c}{n_{water}}$

$\therefore$ $v_{water}=\frac{3\times {10}^8}{\left(4/3\right)}=2.26\times {10}^8$ m/s