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4.3: Luz polarizada
https://espanol.libretexts.org/Matematicas/Algebra_Abstracta_y_Geometrica/%C3%81lgebra_Geom%C3%A9trica_Aplicada_(Tisza)/04%3A_C%C3%A1lculo_espinor/4.03%3A_Luz_polarizada
\[\begin{array}{c} {\tan \alpha = \frac{\tan \frac{\alpha}{2}+\tan \frac{\alpha}{2}}{1-\tan^{2} \frac{\alpha}{2}} = \frac{\frac{\lambda-a_{11}}{a_{12}}+\frac{a_{12}}{\lambda-a_{22}}}{\frac{\lambda-a_{... $\begin{array}{c} {\tan \alpha = \frac{\tan \frac{\alpha}{2}+\tan \frac{\alpha}{2}}{1-\tan^{2} \frac{\alpha}{2}} = \frac{\frac{\lambda-a_{11}}{a_{12}}+\frac{a_{12}}{\lambda-a_{22}}}{\frac{\lambda-a_{11}}{\lambda-a_{22}}}}\\ {= \frac{(\lambda-a_{11})(\lambda-a_{22}) \frac{1}{a_{12}}+a_{12}}{a_{11}-a_{22}} = \frac{2a_{12}}{a_{11}-a_{22}}}\\ {= \frac{2p_{1}p_{2} \cos \phi}{p_{1}^{2}-p_{2}^{2}} = \frac{\sin \theta \cos \phi}{\cos \theta} = \tan \theta \cos \phi} \end{array} \label{EQ4.3.24}$

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