= Malus' law
{c}
{title2=$I=I_0\cos^2\theta$}
An ideal linear polarizer transmits the fraction $\cos^2\theta$ of incident linearly polarized light when its axis makes angle $\theta$ to the polarization. For a single photon, the corresponding conditional transmission <probability> is $|\langle\theta|0\rangle|^2=\cos^2\theta$, by the <Born rule>; rejection has probability $\sin^2\theta$. The classical field calculation projects its electric-field amplitude onto the transmission direction and squares that amplitude to obtain <intensity>. This is a conditional probability given the incident polarization and is not automatically the joint probability of passing one analyzer and failing another.
Back to article page
