Brewster's angle, dipole radiation and refraction

[Aetholite]

So I was wondering how it is possible that there will be no p-pol light reflected when the refracted light is at 90 degrees to the reflected light (so incoming light is at Brewster's angle).

The Brewster's angle was explained to me by saying that the electrons in the medium radiate light (EM-waves), because they osciallate due to the incoming light wave. This radiation is zero in the direction of the electron (dipole) oscillation, thus when the osciallation direction is the same direction as the reflected light would be, no light would be radiated in that direction, and thus no reflection would take place. This being the case only for p-pol light.

But my question is: Doesn't this imply that the electrons oscillate at a diferent angle (refraction angle) and not oscillate at the same angle as the incoming light? I thought the refraction angle was due to the superposition of radiated light from these electrons and not already present at each individual electron. If that is the case, why would electrons oscillate at a different angle (refraction angle) in the receiving medium than they do in the incidence medium?

Could someone explain to me how the brewster angle and refraction work on a miscroscopic level, without it depending on a macroscopic interpretation of light refraction.

 

[tech99]

The incoming light changes direction because it slows down in the second medium. That is Snell's Law and not part of electromagnetics (it also happens with sound, for instance).
The new light beam is now in a direction perpendicular to the Brewster Angle, so you are correct, the E vector of the refracted ray is edge on to the reflected ray, giving zero amplitude for the parallel polarisation.
There is a lecture by Prof Lewin at this URL which does it more formally by deriving the Fresnel equations. These give us the intensity of each ray based on the incident angle and the refractive indices.

 

[kuruman]

Could someone explain to me how the brewster angle and refraction work on a miscroscopic level, without it depending on a macroscopic interpretation of light refraction.

"The polarization of freely propagating light is always perpendicular to the direction in which the light is travelling. The dipoles that produce the transmitted (refracted) light oscillate in the polarization direction of that light. These same oscillating dipoles also generate the reflected light. However, dipoles do not radiate any energy in the direction of the dipole moment. If the refracted light is p-polarized and propagates exactly perpendicular to the direction in which the light is predicted to be specularly reflected, the dipoles point along the specular reflection direction and therefore no light can be reflected."

From https://en.wikipedia.org/wiki/Brewster's_angle