With regards to light splitting up when shone through a triangular prism, why does the velocity of the light wave depend on its frequency (hence causing this phenomenon)?
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When the light is traveling through the prism, it is actually continually absorbed and re-emitted by the atoms in the material. There is a very slight delay between emission and absorption, which is why the speed of light is less in the material than in the vacuum. However, the length of that delay depends on the specific absorption modes, which means it depends on the wavelength.