Two different mediums can have equal index of refraction? In other words: given a certain medium, is light's phase velocity unique?
 A: Two media can have equal indices of refraction. For example, you could pick the densities of two different gases so as to make their indices of refraction equal. You could do the same thing with different liquids containing properly chosen concentrations of solutes.
A: Well it is a very popular, and useful property of some optical glasses used in lens design.  If you look at a glass catalog from say Schott or Hoya, and others, you will be able to find from their data, pairs of glasses, which have the same refractive index (n) at some wavelength (He d line or Na D line) but have different dispersions (V value) or change of index with wavelength.
So you can include a lens in your design, that has that common index, to achieve some property.  But you then split the lens into two (cemented) elements, one from each of the chosen pair.
Since both glasses have the same d index, it doesn't matter at all, what the common cemented surface radius of curvature is, so the common surface is invisible or "buried".
But now if you investigate the total lens properties, as a function of wavelength, for chromatic effects, you find that the common surface radius is a very useful control of chromatic aberrations, with virtually no effect on the monochromatic aberrations.  Well it will affect chromatic variation of monochromatic aberrations, (like spherical, coma, astigmatism, and distortion) but those are higher order aberrations, than the Seidel aberrations.  so the short answer is yes.
A: I'd say, given a certain media, light's phase velocity is not unique, because there is aways some dispersion (unless the medium is a vacuum).
