The intensity of polarized light after passing through a polarizer is given by [tex]I=[/tex] [tex]Iocos^2\alpha[/tex]
Malus's law says that when a perfect polarizer is placed in a polarized beam of light, the irradiance, I, of the light that passes through is given by
[tex]I = Io cos^2 \alpha[/tex]
where Io is the initial intensity and
[tex]\alpha[/tex] = is the angle between the light's initial polarization direction and the axis of the polarizer.
A beam of unpolarized light can be thought of as containing a uniform mixture of linear polarizations at all possible angles. Since the average value of [tex]cos^2\alpha[/tex] is 1/2, the transmission coefficient becomes
I/I0 =1/2.
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