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I am reading an optics book (Physics of Light and Optics by Peatross and Ware) that asserts this:

A beam of light can always be considered as an intensity sum of completely unpolarized light and perfectly polarized light:

$$I=I_{Pol}+I_{Un}$$

How does this marry with the superposition principle? Why can we just add the intensities?

Kyle Kanos
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Yossarian
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    This means that every $2 *2$ density matrix $\rho$, with $Tr (\rho)=I$ may be written : $\rho = I_{pol} ~\rho_{Pol} + I_{Un} ~\rho_{Un}$, where $Tr(\rho_{Pol})= Tr(\rho_{Un})=1$, with $I_{pol}+I_{Un}= I$, and where $\rho_{Un}$ is the diagonal matrix Diag($1/2,1/2$), and $\rho_{Pol}$ is the density matrix corresponding to some pure normalized state. – Trimok Jan 01 '14 at 19:30
  • @Trimok That's a really great take on it. I think you should make this an answer: I was going to recommend reading great swathes of Born and Wolf "Principles of Optics", but if one has studied QM and the density matrix, your statement is succinct and gets a subtle idea across easily. Otherwise, one needs to bang on about ergodic random processes and so forth - the classical description in my experience is really hard to explain: I don't think I have ever done it without thoroughly confusing the listener! – Selene Routley Jan 02 '14 at 12:05
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    Dear William, if you have studied QM and ken the density matrix, then @Trimok 's description is the best I've read. Otherwise a classical description is part of my answer here, considerably harder to understand IMO. One of those few cases where a QM description really adds something to the classical description. – Selene Routley Jan 02 '14 at 12:07
  • thanks for the comments, yes, I know a little about density operators in QM and I liked your comment Trimok. – Yossarian Jan 02 '14 at 16:13

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