Why does white light entering a prism leave a rainbow?
When light hits the prism at an angle θ₀, the exiting angle is given by sinθ = sinθ₀ /𝑛
Different colors have different 𝑛 (in glass)
So each color will exit the prism with a slightly different angle θpic.twitter.com/yIsrbkk76p
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But ELI5 why different colors/frequencies have different n’s?
Depending on what level of description you're looking for it's rather nontrivial. But you you can think of it as the atoms of the glass have particular "resonant" frequencies.. Being made of charged particles, they will interact with the light in slightly different ways
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That’s probably the best particle interpretation. To me it seems cleanest to think in terms of waves here though.
Boundary conditions require wave to be continuous at boundary, and since wave velocity changes upon entering medium, wavelength must change? -
These are all consistent, but I prefer to think about them more fundamentally
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In a sufficiently homogeneous medium it's modeled phenomenologically as a dipersion relation. The model for light waves in a vacuum is nondispersive, not so in glass. Water waves are also dispersive.
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The dispersion relation is usually expressed as a relationship between frequency and wavenumber as reflected in a frequency dependent index of refraction.
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