Thanks to Willebrord Snellius (1580–1626).

λ1n1 = λ2n2
When light travels from one transparent medium to another, its frequency cannot change, but its phase speed does. This requires its wavelength to change, so that the frequency times the new wavelength is equal to the new phase speed.

Indices of refraction can vary from a hair above 1.0 up to 2.5 or more.

Because of a resonance in the ultraviolet, the index of refraction for materials that are transparent to visible light increases as the wavelength decreases.  Thus n(λ) is always largest for violet light and smallest for red light.

Recently physicists have been exploring the construction of so-called "meta-materials," which have negative index of refraction! There are an enormous number of potential technological applications for such materials, which usually look like huge arrays of microscopically tiny antennas.