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its that light is supposed to have the same energy of hf always where h is plank's constant and f is the frequency ot the light. since it has the same energy, everywhere, frequency has to not vary.
so the only thing that gets affected in different mediums is the wavelength, which is something like lamda1(n1) = lamda2(n2) where lamda is wavelength and n is the refractive index of the medium.
This is the result of interference with atoms and molecules in the medium so that it takes more energy to travel a given length in a higher refractive index medium than a lower one.
once you exit the high index medium, the same energy lets you "speed up" again since you're don't have that extra resistance.
sort of like if you're driving and aim to keep the same rpms throughout a long drive, you must slow down going uphill and speed up going down hill, but once you're level again you'll be at the same speed as before if you always try to keep your rpms constant.
of course as far as light is concerned, there is no downhill. there are flats and different degrees of steepness of your uphills
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