Index of Refraction and Wave Speed

Light slows down inside glass or water because it keeps interacting with the atoms in the material, getting absorbed and re-emitted in a way that delays its net progress. The index of refraction, n, measures this directly: n = c/v, where c is the speed of light in vacuum and v is its speed in the medium. A bigger n means a bigger slowdown. The instant light exits back into air, it speeds right back up to its vacuum value, because the slowdown only happens while it is interacting with the medium's atoms.

Frequency is set by the source emitting the light, and nothing about entering a new medium changes how fast that source is oscillating, so frequency never changes at a boundary. Speed does change, and because speed = frequency x wavelength, wavelength has to change too, by the same factor as speed. That gives the key relation lambda_medium = lambda_vacuum / n: a higher index squeezes the wavelength down proportionally. Speed drops by the same factor, v = c/n.

This is the quiet mechanism behind Snell's law in the next topic: the bending of light at an interface comes directly from this change in speed between two media. Keeping straight which quantity is fixed (frequency) and which two are linked and changing (speed and wavelength) is what makes refraction problems solvable instead of confusing.