How do polarizers work?
A polarizer is an optical filter that allows only the oscillations of light parallel to its transmission axis to pass through. The device blocks almost half of the energy of unpolarized light that is incident on a polarizer. Here, only those sections vibrate which are perpendicular to the transmission axis, thus producing linearly polarized light. This is the reason the intensity of light from a polarizer is half that of the incoming unpolarized light intensity.
For unpolarized light incident on a polarizer, the transmitted intensity is given by $$
I= \frac {I_{0}}{2}
$$