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I was hoping someone could help me with understanding why a row of polarizes reflects a light wave when the whole row is the same length as the wavelength of the light.

Liquid crystals

I pretty much get the physics behind the rest, just don't understand this little part. Why only the light of that wavelength and does this also apply for light coming in at a different phase than the crystals?

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2 Answers

The picture is misleading because it makes it look as if all the reflection occurs at the surface. In fact, reflection is occurring throughout the volume, and only for a particular wavelength will all the reflections add "in phase", for other wavelengths they will partially cancel each other.

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But how exactly? The light with the correct wavelength passes trough unafected, while the rest gets polarized and whatnot. After that most of these crystals have a black layer to absorb everything that comes trough, but why doesn't the light of the correct length get absorbed? –  Coolcrab Jul 16 '12 at 18:58
    
Each layer partially reflects light, partially transmits. If the wavelength and polarization are right, the reflections enhance each other. It's kind of like Bragg reflection. –  user1631 Jul 16 '12 at 20:24
    
Thanks, I understand now! –  Coolcrab Jul 17 '12 at 8:37
    
actually, reflection only happens at surfaces, namely at borders of two phases with different refractive indices. –  gigacyan Jul 17 '12 at 17:13
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The question is somewhat mixed so I will try to restate it as I understood it and you should correct me if I got it wrong.

As I see, the question here is: why does a thin film of liquid crystals changes its color as it gets colder or warmer?.

The answer to this question is interference. The light is reflected from both the top and the bottom surface of the film and the two reflections will interfere with each other. If for some wavelength accumulated phase difference between reflections is close to a multiple of $2\pi$ then the interference is constructive and this color will be enhanced in reflecting light.

The phase difference difference depends on the path length, and when the film gets thicker, the wavelength of reflected light will shift towards red.

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What you say would be correct for reflection from a film of homogeneous material, but that is the case under consideration here. The resonant condition in question is dependent on the pitch of the cholesteric liquid crystals, not the total thickness of the sample. –  user1631 Jul 17 '12 at 21:25
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