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

Answer

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

Explanation

If `v_(1)` is the velocity of light in vacuum, `v_(2)` is the velocity of light in glass and `v_(3)` is the velocity of light in water then, absolute refractive index of glass i.e., 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_(2))=(4)/(3)" ......(ii)"`
`therefore` Refractive index of glass with respect to water
`""_(g)n_(w)=(v_(3))/(v_(2))`
`=(v_(1))/(v_(2))xx(v_(3))/(v_(1))" "`....(Multiplying and dividing R.H.S. of equation by `v_(1))`
`=(3)/(2)xx(3)/(4)" "` .....[From equations (i) and (ii)]
`=(9)/(8)`