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In the explanation of Brewster window, wherever in the literature I have looked up, it considers the unpolarized light with only two polarization components: the s and p components.

But, in case of unpolarized light, the electric field oscillates in all directions, so at Brewster angle the p polarized light will not be reflected, I understand. But what about the other electric field components, other than s one? I suppose they will be reflected too. If this is the case, how does it come that the reflected light is completely polarised?

Thanks! enter image description here

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Every linear polarization can be decomposed along two directions, one perpendicular to the other.

You correctly know that one of them will be partially reflected and partially transmitted, while the other completely transmitted. For a linear polarization along one of these two directions, you have a correct understanding of what is happening. For every other direction, you can think at it as the superposition of two components, one in each direction; therefore part of it (corresponding to the component in the direction in which we have also reflection) will be partially reflected and partially transmitted, while the other part (corresponding to the component in the direction in which we have only transmission) will be transmitted.

This results in a linear polarization of the reflected wave.

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