First, the analytic expressions are derived that describe some properties of the Poincaré sphere that are related to the coherent sum of two waves having different polarizations. Then these expressions are used to obtain the differential equation that describes the evolution of the state of polarization of radiation propagating in a medium that is nonuniform, birefringent, optically active, and dichroic. Finally, an important example is presented: that of a magnetized plasma in which particle collisions are not negligible, such as the earth's ionosphere or certain laboratory plasmas. The evolution equation is the basis of plasma polarimetry.