Monochromatic rays of light coming from vacuum are refracted in a medium of refractive index `mu` . Show that the ratio of the wavelength of the incident ray that of the refracted ray is equal to the refractive index of the medium.

Explanation

Suppose the wavelength of light in vacuum is `lambda` and its velocity is c. The corresponding values in a medium of refraction index `mu "are" " " lambda and c. . Frequncy of light is `v. The frequency of light remains the same in all media.
So velocity of light in vacuum, c = `vlambda` and velocity of light in the referred medium `c. = vlambda.`.
Now refractive index of the medium,
`mu = ("velocity of light in vacuum")/("velocity of light in the medium") = (c)/(c.) = (vlambda)/(vlambda.) = (lambda)/(lambda.)`