Calculate refractive index from angles.
Measuring the incidence and refraction angles at a boundary determines the refractive index of the second medium, because Snell's law fixes the ratio of the sines to the inverse ratio of the indices. The index is also the factor by which light slows in the material, so dividing the vacuum speed of light by it gives the propagation speed — and once the index is known, the critical angle for total internal reflection follows immediately.
Refractive index from measured angles
n2 = n1 x sin(incidence) / sin(refraction); v = c / n2; critical angle = arcsin(n1 / n2)
Vacuum is exactly 1, air 1.0003, water 1.333, crown glass about 1.52, sapphire 1.77 and diamond 2.417. Diamond's high index gives it both a small critical angle of 24 degrees and its characteristic brilliance.
Because the material's electronic response varies with frequency. That dispersion is why a prism separates white light and why lens designers combine glass types to cancel chromatic aberration.
The wave's phase and group velocities are genuinely reduced, yes, and the index is defined by that ratio. Individual photons still travel at c between interactions; the slowdown comes from repeated absorption and re-emission by the medium's electrons.