Question

The absolute refractive indices of glass and water are 4/3 and 3/2, respectively. If the speed of light in glass is 2 × 10⁸ m/s, calculate the speed of light in

(a) vacuum (b) water

Answer 1

Refractive index of glass, η_g = 4/3

`thereforeeta_g="Speed of light in vacuum"/"Speed of light in glass"`

`4/3="Speed of light in vacuum"/(2xx10^8)`

`"Speed of light in vacuum "=(4xx2xx10^8)/3=2.6xx10^8"m/s"`

`"Refractive index of water,"eta_w=3/2`

`eta_w="Speed of light in vacuum"/"Speed of light in water"`

`3/2=(2.6xx10^8)/"Speed of light in water"`

`"Speed of light in water" = 1.73 xx 10^8 "m/s"`

Because the information provided is wrong, ideally the speed of light in vacuum is 3 × 10⁸ m/s and the speed of light in water is 2.25 × 10⁸ m/s.

The correct solution is

 

`"Refractive index of glass,"eta_g=3/2`

`"Refractive index of water,"eta_w=4/3`

`"Refractive index of glass,"eta_g="Speed of light in vacuum"/"Speed of light in glass"`

`3/2="Speed of light in vacuum"/(2xx10^8)`

`"Speed of light in vacuum "=(3xx2xx10^8)/2=3xx10^8"m/s"`

`"Refractive index of water, "eta_w=4/3`

`eta_w="Speed of light in vacuum"/"Speed of light in water"`

`4/3=(3xx10^8)/"Speed of light in water"`

`"Speed of light in water "=(3xx3xx10^8)/4`

`"Speed of light in water "=2.25xx10^8"m/s"`