The polarizing angle θpol is the angle of incidence at which an incident wave of arbitrary polarization becomes linearly polarized on reflection. In terms of the reflection amplitudes it is given by rpprss-rpsrsp=0. We show that it may be obtained by the solution of a quartic equation. This equation is closely related to the quartic that defines the Brewster angle θpp at which rpp is zero, previously obtained. The angles θpol and θpp are compared and contrasted. A method of identifying the physical root or roots of each quartic is given. Index matching enhances the difference between θpol and θpp.
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