Instructor's Notes


(1) Explain the observations of section 6, part 7, in particular, show how the "picket fence" analogy is wrong and misleading, and how the vector model does give correct results. Use diagrams.

The picket fence analogy predicts that the third polarizer between crossed ones would transmit less energy than two crossed ones alone. Yet, as the picture shows, more light energy gets through three arranged in this way, than through the two crossed polarizers alone.

The vector model allows quantitative prediction of the intensity as a function of angles (Malus' Law).

(2) Some books suggest that polarization of light represents strong evidence for the wave theory of light (as opposed to a strictly particle theory). To challenge this glib assertion, devise a particle theory (no waves allowed!) which would be adequate to explain the experimental phenomena studied in this experiment. Be creative, but be sure that your model meets the criteria of good physics:

  1. The model must correctly describe known physical facts.

  2. The model must be quantitative.

  3. The model must be testable and potentially refutable by experimental test.

  4. All features of the model must have a clear and precise relation to observables (it must not include any features unrelated to observables).

Do not be prejudiced or limited by any models of light you have already learned.

Even if you are not successful, carry this far enough to show why it would be very difficult to devise such a model.

When the question was asked in a science seminar, of students innocent of science courses, the class evolved an interesting model in which the light particles were shaped like smooth Frisbees and the polarizers had smooth parallel rods. The spacing of the rods was only large enough to allow Frisbees to slip through when oriented just so. However, a misaligned frisbee, being disklike, would strike the polarizer and reorient itself to slide through, provided it weren't entering at 90° to the proper orientation. Actually, to satisfy the law of Malus, they had to assume that an orientation greater than 45° would prevent transmission, and somehow disintegrate the Frisbee into thermal energy!


(1) At Brewster's angle, the reflected ray is perpendicular to the refracted ray. Use this fact to calculate the index of refraction of the glass specimen used to find Brewster's angle. This is how the index of refraction can be determined even for an opaque specimen. The specimen you used may have been totally opaque black glass. How do you suppose the light "knows" the index of refraction of the glass if no light is actually refracted? Isn't index of refraction a "bulk" property of the glass rather than a "surface" property? So if no light gets into the "bulk" of the glass, how can the index of refraction "determine" the Brewster's angle?

Some electromagnetic energy penetrates into the bulk of the material, just under the surface, in the "skin depth." In the classical model, the fields which penetrate just under the surface are determined by the dielectric properties of the material. In the quantum interpretation, absorption and re-radiation from atoms just under the surface do the trick.