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 \[c = f \lambda\]