Electromagnetic waves in media

In vacuum, Maxwell's equations fix the speed of an electromagnetic wave at exactly c. Inside a material, the wave still travels through the same vacuum between atoms, but the atoms' electrons feel the oscillating field and oscillate along with it, re-radiating their own electromagnetic waves that lag slightly behind the driving field. The net effect of the original wave plus this cloud of delayed re-radiation is a combined wave that appears to travel slower than c — not because light itself has changed, but because the material's response builds in a delay at every point along the way.

That slowdown is what the refractive index n measures: n = c/v, the factor by which a material's electrons slow the wave's apparent progress. A higher refractive index means a slower speed inside that material, full stop — despite the word's association in casual usage with "bending", n is defined by speed, and the bending of light at an interface (what most people picture first) is itself a consequence of that speed change, not a separate fact.

One quantity survives the crossing into a medium unchanged: frequency. It is set by whatever oscillates the wave in the first place — the source — and every atom in the material that responds to the wave must oscillate at that same driven frequency, so nothing downstream can alter it. Since v = fλ and v drops while f holds fixed, wavelength must shorten to compensate — light turning from blue to violet is a change of source, never something a medium can do to a wave passing through it. This is the standard trap in numerical problems: reach for "the wavelength changed, so the frequency must have too" and the answer comes out wrong, because it is precisely the frequency that cannot change.