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 x 10^{14} Hz, find the wave number of light in glass.

[Velocity of light in air c = 3 x 10^{8} m/s]

#### Solution

Given: μ_{g }= 1.5, n=4 × 10^{14}Hz, c = 3 × 10^{8}m/s

The wavelength of light incident on glass from air is

`lambda=c/n=(3 xx 10^8)/(3.5 xx 10^14)=8.571 xx 10^-7 m=8571 xx 10^-10 m=8571Å`

Now, the velocity of light in glass is given from its refractive index as

`mu_g = c/(v_g)`

We also know that velocity is product of frequency and wavelength.

∴`mu=c/(v_g)=(nlambda_a)/(nlambda_g)=lambda_a/(lambdag)`

∴`lambda_g=lambda_a/mu_g=8571 /1.5=5714`Å

Therefore, the difference in wavelength is

`lambda_a-lambda_g=8571 - 5714 = 2857`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/(5.714 xx 10^-7)=1.75 xx 10^6m^-1`