Question

The absolute refractive indices of glass and water are $\frac{4}{3}$ and $\frac{3}{2}$. If the speed of light in glass is $2\times {10}^8{ms}^{-1}$, calculate the speed of light in (i) vacuum, (ii) water.

Answer 1

Let $n_g$ be the absolute refractive index of glass.
Let $n_w$ be the absolute refractive index of water.
Let the speed of the light in glass be $v_g$.
Given : $n_g=\frac{4}{3},n_w=\frac{3}{2},v_g=2\times {10}^{8}m{s}^{-1}$
(i)We know that,
$n_g=\frac{Speedoflightinvacuum}{Speedoflightinthegivenmaterial}=\frac{c}{v_g}$
$\therefore c=n_g\times v_g$
$c=\frac{4}{3}\times 2\times {10}^8=2.67\times {10}^{8}m{s}^{-1}$

(ii) Also, $n_w=\frac{c}{v_w}$
$\therefore v_w=\frac{c}{n_w}=\frac{2.67\times 2\times {10}^8}{3}$
$v_w=1.78\times {10}^{8}m{s}^{-1}$.