Why the Assumption of an Impulse Acting on Light May Have Worked

  If one looks at the change in phase in the plane of refraction along the boundary between the two media one sees that the two components of the wavevector are the same for both wave functions thus enabling us to match them along this line.

When we tried to explain refraction by the assumption of a vertical impulse acting on photons at the boundary we inadvertently assumed that the component of the wavevector on the boundary in the plane of refraction remained unchanged since the momentum of the photon is proportional to its wavevector.