Speed, Frequency and Wavelength of light in Different Media

In different matrials, light travels at different speeds,
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
$c = f \lambda$ 