Calculate the refractive index of water with respect to glass and refractive index of glass with respect to water, if speed of light in water and glass is `2.2 xx10^(8)" m/s and "2xx10^(8)" m/s"` respectively.

Answer

i. Refractive index of glass w.r.t water is 1.1
ii. Refractive index of water w.r.t glass is 0.909.

Explanation

Given : Speed of light in water `(V_(w)) =2.2xx10^(8) m//s,` speed of light in glass
`(v_(g))=2xx10^(8) m//s`
To find i. Refractive index of glass w.r.t water `(""_(g)n_(w))`
ii. Refractive index of water w.r.t glass `(""_(w)n_(g))`
Formulae : i. `""_(2)n_(1)=(v_(1))/(v_(2))`
ii. `""_(1)n_(2)=(1)/(""_(2)n_(1))`
Calculation : From formula (i).
`""_(g)n_(w)=(v_(w))/(v_(g))`
`=(2.2xx10^(8))/(2xx10^(8))`
`=1.1` From formula (ii).
`""_(w)n_(g)=(1)/(""_(g)n_(w))`
`=(1)/(1.1)`
`=0.909`.