Determine the change in wavelength of light during its passage from air to glass. If the refractive index of glass with respect to air is `1.5` and the frequency of light is `3.5 xx 10^(14)` Hz, find the wave number of light in glass.
[Velocity of light in air (c) `= 3 xx 10^(8) m//s`]

Explanation

Given : `mu_(g) = 1.5 , n = 3.5 xx 10^(14) Hz, c = 3 xx 10^(8) m//s`
The wavelength of light inident on glass from air is
`lambda_(a) = c/n = (3 xx 10^(8))/(3.5 xx 10^(14)) = 8.57142xx 10^(-7) m`
`= 8571.42 xx 10^(-10) m = 8571.42Å`
No, the velocity of light in glass in given from its refractive index as
`mu_(g) = c/(v_(g))`
We also know that velocity is product of frequency and wavelength.
`:. mu_(g) = c/(v_(g)) = (nlambda_(a))/(v_(g)) = (lambda_(e))/(lambda_(g))`
`:. lambda_(g) = (lambda_(a))/(mu_(g)) = (8571.42)/(1.5) = 5714.28 Å`
Therefore, the difference in wavelength is
`lambda_(a) - lambda_(g) = 8571.42 - 5714.28 = 2857.14 Å`
The wave number is the reciprocal of the wavelength.
Therefore, the wave number in glass is
`barlambda_(g) = 1/(lambda_(g))`
`:. barlambda_(g) = 1/(5714.28xx 10^(-10))`
`= 1.75 xx 10^(6) m^(-1)`
`= 1.75 xx 10^(6) m^(-1)`