Does the frequency of light change when it travels across an interface between two media? What happens to the light wavelength and the light velocity at the interface?
I've gotten different answers some say all three change and some say frequency is constant or some say that the wavelength is constant...
What's the right answer?
Answer
Frequency is constant. If it were otherwise, you would have more (or fewer) wave crests hitting the interface per unit time than leaving it, which would lead to some sort of pileup that gets worse and worse as time progresses. Another way to think about it is the atoms/electrons/electric field lines/whatever at the interface respond immediately to their neighbors (the wave is essentially continuous), even if those neighbors are in a different medium.
Wavelength can change, and it does so in such a way that $f \lambda = c/n$ at all locations. Here $f$ is the frequency, $\lambda$ is the wavelength, $c$ is the speed of light in vacuum, and $n$ is the index of refraction. As you can see, going from air ($n \approx 1$) to glass (say $n = 1.4$) will result in the wavelength of optical light to decrease by a factor of $1.4$. Also note that in general $n$ can depend on $f$, leading to colors dispersing as in rainbows and chromatic aberration.
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