Physically, the amount of refraction depends on the change in speed of the wave as it crosses the boundary between the two materials.
The change in speed, in turn, can depend on the wavelength.
In the case of light, for example, the change in speed, and therefore the amount of refraction, when it passes into glass, depends on the wavelength.
Blue light is refracted more than red.
This is because blue light changes speed (slows down) more than red.