Question

The velocity of light in glass whose refractive index with respect to air is $1.5$, is $2\times {10}^8{\text{m s}}^{-1}$, and in a certain liquid, the velocity of light is found to be $2.5\times {10}^8{\text{m s}}^{-1}$. Find the refractive index of the liquid with respect to air. [2 marks]

Answer 1

Refractive index ($n$) is inversely proportional to velocity ($v$).
Let $n_i=$ Refractive index of liquid w.r.t air
$n_g=$ Refractive index of glass w.r.t air $=1.5$
$v_i=$ velocity of light in liquid $=2.5\times {10}^8{\text{m s}}^{-1}$
$v_g=$ velocity of light in glass $=2\times {10}^8{\text{m s}}^{-1}$ [1 mark]

$n\alpha \frac{1}{v}$

$⟹\frac{n_l}{n_g}=\frac{v_g}{v_l}$

$⟹\frac{n_l}{1.5}=\frac{2\times {10}^8}{2.5\times {10}^8}=\frac{2}{2.5}=\frac{20}{25}=\frac{4}{5}$

$⟹n_l=1.5\times 0.8=1.5$

$\therefore$ The refractive index of the liquid with respect to air is $1.5$. [1 mark]