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Electromagnetic waves travel as vibrations in the magnetic field and electric fields however since the magnetic field and electric field is perpendicular to each other, does this mean a polraised light ray will have vibrarions travelling in just one of the two fields?

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  • $\begingroup$ Both are filtered by the same factor. The ratio $E/B$ has to be constant to the speed of light. $\endgroup$ – Yuzuriha Inori Mar 11 '18 at 5:13
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If you consider that the $\textbf{B}$ field is actually not a true vector but an axial vector then it is better to think of it as an anti-symmetric (or skew-symmetric) tensor that in 3 dimensions has only three non-zero components representing a plane of action in which the magnetic force acts on a current element lying in that plane the force being perpendicular to that current element. Looking at it from this point of view a linearly polarized EM wave has indeed its $\textbf{E}$ and $\textbf{B}$ fields oscillate in the same plane, the $\textbf{E}$ field as a line of action and the $\textbf{B}$ field as a plane of action. The plane of action was called by Ampere the "directive plane". This is why it is more revealing to index the field components not as $B_x,B_y,B_z$ but rather as $B_{yz}, B_{xz}, B_{xy}$.

In short, the linear polarizer that is set to be parallel with the directive plane will pass the EM wave completely.

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