The wavelength corresponding to the red line of the spectrum of hydrogen in vacuum is equal to 656

The wavelength corresponding to the red line of the spectrum of hydrogen in vacuum is equal to 656 find the wavelength of the same light in glass if the refractive index of the glass for this light is 1.6.

The refractive index of the medium n is equal to the ratio of the speed of light in vacuum c to the speed of light in the medium V:

n = c / V (1).

On the other hand, both the speed of light in a vacuum and the speed of light in a medium can be represented as the product of the wavelength λ of the light wave by the frequency ν:

c = λν,

v = λсν,

where λ and λc are the wavelengths in vacuum and in the medium, respectively.

The frequency does not change when moving from one environment to another.

Substitute expressions for c and v in (1):

n = λν / λ1ν = λ / λ1;

λ1 = λ / n = (656 nm) / 1.6 = 410 nm.

Answer: The length of the red color in the medium is λ1 = 410 nm (4.1 * 10-7 m).