= Transmission through a sequence of linear polarizers
{title2=$I_{\rm out}=(I_{\rm in}/2)\prod_{j=2}^N\cos^2(\theta_j-\theta_{j-1})$}
For ideal <polarizers> with successive transverse transmission directions $\theta_j$, the <Jones matrix> is the rank-one <orthogonal projection> $P_j=\mathbf u_j\mathbf u_j^{\mathsf T}$. The identity $\mathbf u_j^{\mathsf T}\mathbf u_{j-1}=\cos(\theta_j-\theta_{j-1})$ reduces the transmitted <probability amplitude> analogue, here the optical <complex amplitude>, to a product of projections. For <unpolarized light>, the first element transmits half the incident <light intensity>, giving the displayed product. For a specified incident <linear polarization>, replace the first half-factor with its actual projection.
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