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

(N/A) Given: Refractive index of glass $(n_g)$ = $3/2$,Refractive index of water $(n_w)$ = $4/3$,Speed of light in glass $(v_g)$ = $2 \times 10^{8} \ m \ s^{-1}$.
$(i)$ Speed of light in vacuum $(c)$:
Using the formula $n_g = c / v_g$,we get $c = n_g \times v_g$.
$c = (3/2) \times (2 \times 10^{8} \ m \ s^{-1}) = 3 \times 10^{8} \ m \ s^{-1}$.
$(ii)$ Speed of light in water $(v_w)$:
Using the formula $n_w = c / v_w$,we get $v_w = c / n_w$.
$v_w = (3 \times 10^{8} \ m \ s^{-1}) / (4/3) = (3 \times 3 \times 10^{8}) / 4 = 2.25 \times 10^{8} \ m \ s^{-1}$.