Classical Maxwellian theory shows that the incident wave superimposed with
the secondary waves of the driven dipole oscillators of the medium (all
traveling at the vacuum velocity c) result in the extinction of the
incident wave and the survival of a refracted wave with a phase velocity
of c/n. This statement is known as the Ewald-Oseen extinction theorem and
is derived in the Born & Wolf Optics text.
Ewald showed this for crystalline media in his 1912 dissertation. Oseen
showed it for isotropic media in 1915.