Why is it that the frequency of light remains the constant as it undergoes refraction at the interface of two material mediums?

Ans) If frequencies are dissimilar in different media, vibration of light wave becomes discontinuous at the boundary among different media because rate of vibration (frequency) is dissimilar. Light wave of one ray should be continuous, shouldn't it. Even if wavelengths are dissimilar in different media, light wave can be continuous at the boundary among different media, so to make the wave continuous the frequency will not change.