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If light is passed through two polarizing filters before arriving at a target, and both of the filters are oriented at 90° to each other, then no light will be received at the target. If a third filter is added between the first two, oriented at a 45° angle (as shown below), light will reach the target.

Why is this the case? As I understand it, a polarized filter does nothing except filter out light--it does not alter the light passing through in any way. If two filters exist that will eliminate all of the light, why does the presence of a third, which should serve only to filter out additional light, actually act to allow light through?

Image of three polarizers, target is at the right

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"As I understand it, a polarized filter does nothing except filter out light--it does not alter the light passing through in any way." This is not the case. –  dmckee Apr 22 '13 at 19:08
    
@dmckee: Actually, I'd agree that it only filters out light -- but light at 45 degree polarization really is a (coherent) linear combination of vertically and horizontally polarized light. Projections need P_a P_b = 0 need not mean that P_a P_c P_b = 0. I guess one can quibble about "does not alter the light passing through in any way." –  wnoise Apr 23 '13 at 1:02
    
It is critically important that after passing a polarizer the light has a new well defined polarization regardless of what it polarization state was before. That is a property of the light that has been changed. You can express it in a number of ways but you need to understand the change in order to explain how inserting a third polarize can result in light passing through where none had passed before. –  dmckee Apr 23 '13 at 1:12

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up vote 5 down vote accepted

This link: http://alienryderflex.com/polarizer/ has an excellent explanation; much better than anything I could write here.

Essentially, it says that this occurs because the 45 degree filter outputs a projection of the vertical rays at 45 degrees. This, in turn, has a horizontal component, which the final filter projects in its output.

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Exactly what I was looking for. Thank you! –  Vaindil Apr 22 '13 at 19:05
    
It might be worth pointing out that, although one can explain the effect classically, one can also do the experiment with single photons. In that case, a quantum mechanical interpretation is needed. –  hanno Jan 25 at 0:37
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@hanno very true! But, and forgive me if this sounds at all dismissive, I wish to leave my answer as is because it is more likely that a google searcher will be looking for a brief and succinct explanation to the classical effect. However, I do encourage someone to post a quantum mechanical explanation; that would definitely round out this question nicely. –  Jim Jan 26 at 14:24

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