electromagnetism - Simple, nonmathematical argument for partial polarization by reflection

I'm teaching calculus-based electricity and magnetism with a sequence of topics in which students learn the basics of electromagnetic waves before the semester in which they get a more general introduction to topics such as wave kinematics, reflection, inverting and uninverting reflections, partial transmission, the optical density, and refraction. They also learn this topic before we do the electrical properties of materials, so they know the distinction between a conductor and an insulator, but they don't know about dielectric constants and so on.

I'm having them do simple experiments with polarizing films and calcite crystals, which works fine as a hands-on way of making sense of the geometry of an electromagnetic plane wave. I also have them look at their cell phones through the polaroids and also at glancing reflections from tabletops in order to see that the reflections are partially polarized.

For students at this stage, is there some very simple hand-waving argument I can present as to why reflections should be at least partially polarizing when the direction of incidence is not normal? Obviously it's easy to show by symmetry that for normal incidence, there is no polarization. I think it would be way too much for students at this stage to present a full treatment of the incident, reflected, and refracted waves with superposition and matching of boundary conditions. I'm thinking that there may be some conceptual simplification possible if one considers the case of an extreme grazing angle, and if we don't care about a detailed quantitative result for the amount of polarization, Brewster's angle, etc. Is there perhaps some simplification that can be made in the case where the surface is highly absorptive? My students do know about dipoles. Is there some simple argument that gives a qualitatively correct result if you treat the surface as a sheet of dipoles?

Answer

Quite simple approach is the scattering model, which considers reflected and transmitted wave as a scattering pattern by the dipoles induced in the second medium. This model is originally due to Sagnac, but it has been included in a number of textbooks. A good resource for this model is a paper

• Doyle, W. T. (1985). Scattering approach to Fresnel’s equations and Brewster’s law. American Journal of Physics, 53(5), 463-468, doi:10.1119/1.14201.

From the paper:

In the usual scattering model of Brewster's law the reflected beam is created by oscillations of the induced dipoles in the second medium, driven by the electric field of the transmitted wave. When the incident wave is $p$-polarized, the reflected beam has zero intensity at Brewster's angle where the reflected and transmitted beams are mutually perpendicular. Since the transmitted beam is transverse, the axes of the induced dipoles then point in the direction of the reflected beam, and a dipole cannot radiate along its own axis. In this model no Brewster angle can occur with $s$-polarized incident waves, because the induced dipoles are always perpendicular to the direction of the reflected beam and each dipole radiates isotropically in its own equatorial plane.

The paper further extends the original model to also include induced magnetic dipoles, and offers elementary derivation of Fresnel's equations and Brewster's law.

One thing the paper emphasizes is that all of the dipoles in the media are contributing to the reflected beam. So, “a sheet of dipoles” would be a wrong model for the situation.