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,

`"n"_"g" = "v"_1/"v"_2 = 3/2`    ...(i)

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

`"n"_"w" = "v"_1/"v"_3 = 4/3`   ...(ii)

∴ Refractive index of glass with respect to water,

_gn_w = `"v"_3/"v"_2`

`= "v"_1/"v"_2 xx "v"_3/"v"_1`  ....(Multiplying and dividing R.H.S. of equation by v₁)

`= 3/2 xx 3/4`   ...[From equations (i) and (ii)]

`= 9/8`

The refractive index of glass with respect to water is `9/8`