I just realized that I am not entirely sure as to what happens with the wavelength and the frequency of an optical plane wave when entering for example glass (e.g. monochromatic laser).
The refractive index of a material is given by $n = \frac{c_0}{c}$, the Helmholtz equation tells us: $k_n = n\frac{\omega_0}{c_0}$ (and the group velocity is given by $v_g = \frac{\partial \omega_n}{\partial k_n}$) where the n-indexed variables are related to the medium with refractive index n.
Now using Helmholtz one can derive that $\lambda_n=\frac{\lambda_0}{n}$, meaning the wavelength gets reduced.
On the other hand we would have $f_n\lambda_n=c_n$, implying $f_n=\frac{c_n}{\lambda_n}=\frac{\frac{c_0}{n}}{\frac{\lambda_0}{n}}=\frac{c_0}{\lambda_0}=f_0$
This in turn would imply that the frequency of the wave remains the same.
I am somehow in need of a sanity check as to whether my deduction makes any sense or not.
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