Glass slows red light less than blue, because the glass has resonances in the ultraviolet that blue sits closer to. So a prism does not separate white into colours; it separates the colours that were already there, each travelling at its own speed and bending by its own amount.
Descartes gave the law of refraction a geometrical explanation in 1637 — light travels faster in air and slower in glass, and the bend is the wavefront simply running into a slower medium. The law itself had been known for a thousand years in China, and Snell had it in the Netherlands in 1621.
But the law does not explain a prism. A single index cannot say why a beam of white light spreads into a fan, because by the law of refraction a single ray of a single index goes to a single place. The answer came from Newton, who was not the first to notice the colours — Descartes had, and had thrown it out as a curiosity — but the first to insist that the colours were in the light all along.
Cauchy's formula n = A + B/λ² fits the index of every transparent solid over the visible range. A is the part that never changes; B is the amount of dispersion, and it is the only thing that matters when you are choosing a glass. Crown glass barely disperses, so it is used for lenses. Flint glass disperses hard, so it is used for prisms, where you want the colours apart.