### Some More Bi-Curious Behavior

Some time ago I posted some pictures of stress-induced birefringent materials viewed with polarizing filter and a polarized source. Well, I’ve been playing around some more (partly because of the sunstone story).

A quick reminder: birefringence is the effect that of having a different index of refraction along different axes of the material. Linearly polarized light that enters at any angle to the axes will be “broken down” into its two components, and each component will propagate at a different speed, because the propagation speed depends on the index. (This introduces a lag between the two components and for the right thickness, you can get them 90 degrees out of phase, giving you circularly polarized light) Since index also depends on wavelength, this effect will vary for different colors of light. In addition, the amount of stress will vary the amount of birefringence. The end result is that when you filter the outgoing light with another polarizer, you will eliminate any colors depending one their polarization. The transmitted intensity through a polarizer varies as $$cos^2theta$$ so anything close to 90º will be strongly filtered out, but wavelengths/colors close to 0º (or 180º, 360º, etc.) will be transmitted. The result is very Rainbowy.

Here’s a petri dish (sans Robert Petrie). It looks like there’s a strong stress point in the upper left, which has sort of radiated through the whole dish.

Here’s a blank from a CD spindle

The black background is because the polarizing filter is crossed with the source (an LCD monitor) and no light gets through which hasn’t been rotated some amount. If I rotate the filter to be parallel, only light which has been rotated close to 90º gets blocked

You can see that the same regions are affected (and unaffected). There’s also an obvious Moiré pattern in this picture, which is aliasing from the digital source and camera.

One other curious thing: here’s a (different) blank CD spindle in from of the monitor with no polarizer in front of the camera

There’s a rainbow, but without the filter! How can that happen?

Reflection polarizes light, so what I think is happening here* is that there is the polarization rotation, and reflection of the cross-polarized light off of the bottom surface. The reflection is weak (only around 10%) but basically because of this effect the material is acting as its own polarizing filter. This polarizing effect of reflection is why sunglasses are often polarized — you preferentially cut out excess glare (from e.g. standing water or the hood of your car) by eliminating the polarized light, but without making the glasses opaque and eliminating all light.

*edit: I looked again and you also see it with transmission through the disk, but only when viewing at a shallow angle. The effect goes away when using an unpolarized source. So the cause is a little more subtle.

Added: another pic (forgot I had these in the drawer), with the polarizer not quite fully crossed, to give the best color on the spoon