We call polarization the hidden variable because it is a property of light not readily observed with the unaided eye. Everyone is aware of variations in color and brightness, so in teaching about these properties of light we can appeal to observations that everyone has made or can make with little effort. Alas, this is not so with the polarization of light, which to observe requires a bit of effort and, more important, a few simple tools. Once you have fully grasped polarized light, however, you sometimes can observe its manifestations with nothing but your eyes. We recommend that you have polarizing sunglasses or a polarizing filter near to hand as you read this chapter so that you can observe for yourselves some of the consequences of polarization we discuss.
Treatments of polarization in elementary physics textbooks sometimes are misleading, usually incomplete, and sometimes wrong or incomprehensible. And as one moves further from physics, into chemistry, biology, geology, and meteorology, what is bad becomes progressively worse. We once surveyed geology textbooks and reference works for discussions of the colored patterns seen when transparent crystals are interposed between crossed polarizing filters (see Sec. 7.1.6). What we found was mostly confusing and often erroneous.
In previous chapters we noted in passing that electromagnetic waves are vector waves but were able to sidestep this and make physical arguments based on scalar waves. For example, the simple phase difference arguments in Chapter 3, so helpful for understanding scattering by particles, are essentially independent of the vector nature of electromagnetic waves. To understand polarization, however, requires us to face this head on.
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