Physics - why frequency remains constant during refraction???

why frequency remains constant during refraction??

(1)At the boundary/interface of the medium, the number of waves you send is the number of waves you receive, at the other side, almost instantly. Frequency doesn't change because it depends on travelling of waves across the interface.

But speed and wavelength change as the material on the other side may be different, so now it might have a longer/shorter size of wave and so the number of waves per unit time changes.
           


(2)Frequency of light depends on Energy and vice versa  E= hf
Thus to change frequency of light the energy should be changed.
But light is quantised, it can not lose or gain its energy partially, this means that light frequency should not be changed.

(3)At an interface the total energy must add up and this requires the frequency to remain constant outside and inside the medium. On the other hand the wavelength ,lambda, depends on the speed of light in the medium and is reduced by the index of refraction, n.