Because the speed of light,

\[c\]

the frequency \[f\]

and the wavelength \[\lambda\]

are related by the equation \[c = f \lambda\]

it might be throught that the frequency and wavelength both change but this is not the case.In air the speed is

\[c\]

, the frequency is \[f\]

and the wavelength is \[ \lambda\]

In medium 1 with refractive index

\[n_1\]

the speed is \[\frac{c}{n_1}\]

, the frequency is \[f\]

and the wavelength is \[\frac{ \lambda}{n_1}\]

The wave equation

\[c=f \lambda\]

becomes \[\frac{c}{n_1}=f \frac{\lambda}{n_1}\]

We can muliply by

\[n_1\]

on both sides to get \[c = f \lambda\]

If the light then travels through medium 2 with refractive index

\[n_2\]

the speed is \[\frac{c}{n_2}\]

, the frequency is \[f\]

and the wavelength is \[\frac{ \lambda}{n_2}\]

The wave equation

\[c=f \lambda\]

becomes \[\frac{c}{n_2}=f \frac{\lambda}{n_2}\]

We can muliply by

\[n_2\]

on both sides to get \[c = f \lambda\]