It does not matter whether there is a change of medium or there is a change in the speed of light, but the frequency always remains the same. Also frequency, wavelength and speed of light are related to one another by the condition, Speed= frequency times wavelength.

What remains constant during refraction?

Wave speed, frequency and wavelength in refraction

Although the wave slows down, its frequency remains the same, due to the fact that its wavelength is shorter. When waves travel from one medium to another the frequency never changes.

What always remains constant when light is refracted?

In order for the light speed to change, the wave length changes while the frequency remains constant. Thus, the light frequency is the quantity that is constant during refraction of light.