As explained below.
The refractive index
The speed at which crests or the phase of the wave moves is its phase velocity. Speed of light in vacuum is a constant.
Extending the equation for red and violet lights
Dividing one with the other we obtain
Look at the following figure which shows different refractive indecies of light of different colours.
The refractive index of red light is less than that of violet light, as its angle of refraction is less.
Follows that speed of light higher for red than violet in a particular medium other than vacuum.