The speed of light in a medium depends on :

wavelength

Speed of light depends on refractive index of the medium. 

$ v = \frac{c}{\mu}$

Refractive index of a medium depends on wavelength of the light according to cauchy relatin it is $ \mu = A + \frac{B}{\lambda^2}$

Hence the speed of light in a medium depends on the wavelength of light in that medium.