What causes polarised materials to change colour under stress?

Our physics teacher showed the class a really interesting demonstration. He used two polarised filters in opposite orientations, then he took some antistatic tape and stretched it under the two plates. The resulting image was projected on the wall using an overhead projector unit.

Under stress, the originally clear looking tape (as it looked between the polarised filters) turned all sorts of weird colours, and apparently different colors correlate to different levels of stress. What causes this odd effect?

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In case it's not clear from the answers of sigoldberg1 and Flaviu Cipcigan below, the title of this question isn't quite right. It's not "polarised materials" which change color under stress, it's birefringent materials viewed under crossed polarizers. – j.c. Nov 5 '10 at 14:52

Stress implies changing the thickness, therefore the Bragg reflection change. Or shorter: Interference

edit Also, as sigoldberg1 states, Birefringence might occur, too

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Nice short answer. I think you mean 'reflection' though, 'reflexes' doesn't make sense here. – Noldorin Nov 5 '10 at 16:20
@Noldorin: thanks, corrected – Tobias Kienzler Nov 8 '10 at 8:01
@downvoter: no comment? – Tobias Kienzler Dec 6 '10 at 9:49

I agree with the answer given by sigoldberg1 -- it is most probably stress induced birefringence. Bragg scattering would not (at least to first order) change the polarisation of the incoming light beam, thus making the crossed polarisers pretty useless. Also, changes in colour due to Bragg scattering would be observed on reflection and would be angle dependent.

What actually happens in experiments of the type shows in this video is the following:

• The first polariser is used to produce linearly polarised light.
• The second polariser is rotated at 90 degrees with respect to the first, and thus in the absence of any material, no light will pass through (from Malus' law, $cos^2(90^\circ) = 0$
• However, if the material is birefringent (the refractive index depends on polarisation) the polarisation angle of light passing through will be rotated, and this rotation will depend on the wavelength of the light.
• Thus, the final polarisation angle will be different than 90 degrees, and that difference will depend on the wavelength of the light, giving the patterns you see in such an experiment.

Stress induced birefringence is of technical importance due to the fact that "similar effects occur in bent optical fibers, and also due to thermal effects in laser crystals, which can lead to depolarization loss" (ref).

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More likely that the stress induced strain, i.e. stretching of the tape. When the tape stretches, the polymer molecules in it tend to orient or also stretch. This leads to a third layer of polarizing material in the middle, or even birefringence, which makes the colors between the crossed polarizing filters you saw on the screen. At least that's the way I remember it.

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You should have left a comment at my answer, I didn't see your post until now. I should definitely also have included Birefringence in my answer – Tobias Kienzler Nov 8 '10 at 8:11

This is a little off-topic, in that the answers to the question by sigoldberg1 and Flaviu Cipcigan address the relevant physics in plenty of detail already, but I can't resist linking to this video which shows a related phenomenon: beautiful swirls of colors in liquid crystals viewed under crossed-polarizers.

Here the principle is close to what is described by Flaviu Cipcigan, but in the systems of liquid crystals showed in the movie, the stresses arise from the interaction between flow and temperature gradients in the liquid, and instead of birefringence, it's the fact that the molecular orientations themselves are rotating and changing in response to the stresses, and thus letting different amounts of light of different colors through the two polarizers.

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Well they don't change color under stress. It is strain, not stress that distorts the polymer molecules and renders them bi-refringent, typically resulting in a rotation of the plane of polarization. The first (plane) polarizer renders the random light plane polarized. Without the intervening material, the second crossed polarizer then eliminates the only light which was left, leaving darkness (with perfect polarizers)

After insertion of the strained material, the plane polarized light has its plane of polarization rotated by the strain bi-refringence, so some of it now passes through the second crossed plane polarizer. Since the rotation is wavelength dependent, different colors rotate different amounts giving the color fringes.

It is extremely difficult to determine stress in a material. Only strain gives observable changes, that can be measured.

Stress of course has units of Newtons per metre squared, while strain is dimensionless (meters per meter).

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Birefringence. Many substances such as cellophane or antistatic tape have two indices of refraction, a 'fast' axis, and a 'slow' axis, not necessarily at right angles to each other. Minute changes in the thickness of a birefringent material will appear to produce different colors between crossed linear polarizers because different thicknesses of birefringent materials result in different polarization phase angles for different colors of light.

Try it yourself by criss-crossing layers of cellophane tape at different angles, and then view this between crossed linear polarizers. You will see a stained glass effect that changes the color of each different thickness of tape, depending on the angle of the polarizers (rotate them with respect to each other).

This is the principle used instead of stains in polarization microscopes, and also is the trick for making color flat screen television and computer displays (try using a polarizer in front of those, too!)

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