Nothing outruns light in a vacuum. Inside glass, water or diamond, though, light travels slower — and the index of refraction is the receipt. $n = \dfrac{c}{v}$, read aloud n equals c over v. Letter by letter: $c$ is light's vacuum speed, $3.00 \times 10^8\ \mathrm{m/s}$; $v$ is the speed of the light inside the material, also in m/s; and $n$ is the index itself — a speed divided by a speed, so every unit cancels and $n$ carries none at all. It is a naked number, and it can never be less than 1, because that would mean something outran c.

Four values worth carrying in your head: air 1.00, water 1.33, crown glass 1.50, diamond 2.42. Diamond's 2.42 is why it sparkles — light crawls through it at about $1.2 \times 10^8\ \mathrm{m/s}$, gets caught inside bouncing (you will meet that trap in the next lesson but one), and only reluctantly leaves.

One quantity survives the crossing untouched, and it is the one students expect to change: the frequency. The atoms at the boundary are driven at the incoming rate and re-radiate at exactly that rate — a green photon does not enter a window and come out orange. Since $v = f\lambda$ still holds and $v$ has dropped by a factor of $n$, the wavelength must drop by the same factor: $\lambda_n = \dfrac{\lambda}{n}$, where $\lambda$ is the vacuum wavelength and $\lambda_n$ is the squeezed wavelength inside the medium, both in metres. Slower and shorter, same count per second.