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

Because, the intrinsic frequency of light is purely a characteristic of the source of that light wave.

Refraction is the change in direction of a wave due to a change in its medium. It is essentially a surface phenomenon. The phenomenon is mainly in governance to the law of conservation of energy and momentum. Due to change of medium, the phase velocity of the wave is changed but its frequency remains constant. This is most commonly observed when a wave passes from one medium to another at any angle other than 90° or 0°. Refraction of light is the most commonly observed phenomenon, but any type of wave can refract when it interacts with a medium, for example when sound waves pass from one medium into another or when water waves move into water of a different depth. Refraction is described by Snell''s law, which states that for a given pair of media and a wave with a single frequency, the ratio of the sines of the angle of incidence θ₁ and angle of refraction θ₂ is equivalent to the ratio of phase velocities (v₁ / v₂) in the two media, or equivalently, to the opposite ratio of the indices of refraction (n₂ / n₁):

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

thanks a ton!!!!!!!