0

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.

velo
  • 51
  • 1
    Related question: Why doesn't the frequency of light change during refraction? – Thomas Fritsch Oct 17 '23 at 21:29
  • 1
    Frequencies never change when going from one material to another, because the frequency represents the time-dependence of each point in the medium, and a single point (at the interface!) can't have two different frequencies. – march Oct 17 '23 at 21:43
  • @march This makes sense, thanks. So even if the (perpendicularly to the laser beam propagation direction) scattered light of a laser beam in a piece of glass looks green, it does not mean that the laser beam itself is green inside the glass? – velo Oct 17 '23 at 21:49
  • 1
    a nonlinear medium may change the frequency, from a pure tone $\omega_1$it will generate its harmonics $n\omega_1; n=1,2,3...$, and from a pair of tones $\omega_1, \omega_2$ it generates its intermodulation terms $n\omega_1+m\omega_1; n,m=\pm 1, \pm 2, \pm 3,...$, etc. – hyportnex Oct 17 '23 at 22:12
  • 1
    @velo "green inside the glass" does not really mean anything. The quality of being green is a physiologic effect. The colour of light makes sense only inside the eye or actually on the retina. Only the frequency of the light reaching the retina matters for the resuling impression of colour. – nasu Oct 18 '23 at 03:14

0 Answers0