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If I have polarized light and I send through only one polarized glass plane, does the transmission axis matter, or will the intensity be halved no matter what.

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up vote 4 down vote accepted

The axes definitely matter. If you put light through a linearly polarized glass pane, the output light will be entirely polarized along the polarization axis of that pane. The intensity of the output light will be

$$I_{\textrm{out}} = I_{\textrm{in}}\cos(\theta)^2$$

where $\theta$ is the angle between the polarizations of the ingoing light and the pane, and $I_{\textrm{in}}$ is the intensity of the input light.

This all assumes the ingoing light is linearly polarized. If it's not, you can always decompose it into a sum of linearly polarized parts, one parallel to the polarization axis of the pane and one orthogonal. Once you've made that decomposition the output intensity is simply the intensity of the input component that's aligned with the axis of the pane.

Note that if $\theta=\pi/4$ we get $I_{\textrm{out}}=I_{\textrm{in}}/2$.

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