Question

The refractive index of water with respect to air is _aμ_w and of glass with respect to air is _aμ_g. Express the refractive index of glass with respect to water. 

Answer 1

We know that _aμ_w = `"sin of angle in air"/"sin of angle in water"`

= `sin i/sin r`

and _wμ_a = `"sin of angle in water"/"sin of angle in air"`

= `sin i/sin r`

∴ _aμ_g = `"sin i (in air)"/"sin r (in glass)" = 1/(""_gmu_a)`   ...(i)

and _aμ_w = `"sin i (in air)"/"sin r (in water)" = 1/(""_wmu_a)`  ...(ii)

From (i) and (ii)

`(""_amu_g)/(""_amu_w) = (1/(""_gmu_a))/(1/(""_wmu_a))`

= `(""_wmu_a)/(""_gmu_a) = (("sin i (in water)")/("sin r (in air)"))/(("sin i (in glass)")/("sin r (in air)"))`

`(""_amu_g)/(""_amu_w) = ("sin of angle (in water)")/("sin of angle (in glass)") = sin i/sin r = ""_wmu_g`

∴ `""_wmu_g = (""_amu_g)/(""_amu_w)`