Question

If the absolute refractive index of glass and water are 3/2 and 4/3 respectively, what is the refractive index of glass with respect to water?

Answer 1

If v₁ is the velocity of light in vacuum, v₂ is the velocity of light in glass and v₃ is the velocity of light in water then, absolute refractive index of glass, i.e., a refractive index of glass with respect to vacuum,

${\displaystyle {\text{n}}_{\text{g}}=\frac{{\text{v}}_1}{{\text{v}}_2}=\frac{3}{2}}$    ...(i)

Absolute refractive index of water ,i.e., refractive index of water with respect to vacuum,

${\displaystyle {\text{n}}_{\text{w}}=\frac{{\text{v}}_1}{{\text{v}}_3}=\frac{4}{3}}$   ...(ii)

∴ Refractive index of glass with respect to water,

_gn_w = ${\displaystyle \frac{{\text{v}}_3}{{\text{v}}_2}}$

${\displaystyle =\frac{{\text{v}}_1}{{\text{v}}_2}\times \frac{{\text{v}}_3}{{\text{v}}_1}}$  ....(Multiplying and dividing R.H.S. of equation by v₁)

${\displaystyle =\frac{3}{2}\times \frac{3}{4}}$   ...[From equations (i) and (ii)]

${\displaystyle =\frac{9}{8}}$

The refractive index of glass with respect to water is ${\displaystyle \frac{9}{8}}$