Can Fresnel Equations Be Generalized for Arbitrary Polarization of Light?

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Savant13
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Is there a generalized Fresnel equation for the reflection of light with arbitrary polarization (between p and s)?
 
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I hadn't, as not all formalisms involve matrices (as far as I know)
 
The s and p polarizations are considered separately, using the Fresnel equations that you are familiar with. The E-field is then a 2-component vector, the "Jones vector".

Googling "Jones matrix", as Andy suggested, should get you off and running.