The title could be: How Do Colors Appear on a Birefringence Chart?

[Particle-Wave]

I'm not a physics whiz, so please be patient with me!

I understand that when polarized light passes through an anisotropic sample, it bifurcates into the o-ray and the e-eay. The two rays emerge out of phase to each other and when they hit the polarizer, they recombine. Due to the fact that the waves were out of phase, when recombined, it forms a new polarized wave (made up of various wavelengths). What I don't understand is what justifies the colors on the birefringence chart, specifically according to the second figure posted here according to the link posted below:

http://www.microscopy-uk.org.uk/mag...scopy-uk.org.uk/mag/artnov08/rd-crystals.html

Can someone explain figure 2 to me? From what I understand, the retardation of each specific color in the e-wave is different to its corresponding color in the o-ray (for instance, red light for the two waves has a higher retardation (N_o - N_e) than blue light when comparing where they are when the two rays emerge from the crystal). When two corresponding colors combine at the analyzer, some are amplified (constructively), while some are nullified (destructively) and most are somewhere in between. These colors (after having their intensity adjusted due to constructive/destructive interference) are put together and give us the color that we see (depending on where the viewing port is, which relates to sample thickness). Is this correct, or more likely completely incorrect?

Any help would be greatly appreciated. Something tells me that I'm missing something key here.

 

[Andy Resnick]

IIRC, you are referring to a 'lambda plate':

http://www.microscopy-uk.org.uk/mag...microscopy-uk.org.uk/mag/artjan05/bjcomp.html

It relies on a highly dispersive material; this allows the polarization state to be encoded as color. The colors 'wash out' as the thickness/retardation/order increases due to the usual dispersive effects- the orders mix into each other.

Or is this something else?

 

[Particle-Wave]

Oh, I was referring to what happens after the e-wave and o-wave exit from an anisotropic sample at the stage area of a polarized light microscope. From what I understand (probably incorrectly), the individual wavelengths of light in each wave are retarded at different rates. When the two waves recombine, the amplitude for each wavelength is adjusted due to the constructive/destructive interference at the analyzer. All the wavelengths put together with their adjusted intensity gives us the color we see at the eyepiece. I'm just wondering if that is correct. The Michel-Levy Birefringence Chart can tell you how thick the sample is, or what type of sample it is, etc.

 

[Andy Resnick]

I think you are on the right track- let's see if we can step through the reasoning. First, we are illuminating a (thin) birefringent sample using 'white' linearly polarized light. Then, the light passes through a crossed polarizer. What will you see?

 

[pmacias]

I can provide an explanation for the colors seen on a birefringence chart. Birefringence refers to the ability of a material to split a beam of light into two polarized rays, each traveling at a different speed. This phenomenon occurs in anisotropic materials, which have different physical properties in different directions. When polarized light passes through such a material, it is split into two rays, one that travels along the fast axis (o-ray) and one that travels along the slow axis (e-ray). These rays have different refractive indices, meaning that they travel at different speeds and therefore experience different amounts of retardation as they pass through the material.

The birefringence chart, also known as a Michel-Lévy chart, is a way to visualize the difference in refractive indices between the o-ray and the e-ray. The chart typically consists of a series of colored bands, with each band representing a different amount of retardation. The colors seen on the chart are a result of the interference between the two polarized rays as they recombine after passing through the material.

To understand figure 2 on the webpage provided, it's important to know that the chart is created by placing a polarizer and an analyzer on either side of the sample. The polarizer only allows light waves that are vibrating in a specific direction to pass through, while the analyzer can be rotated to allow different wavelengths of light to pass through. When the two polarized rays recombine at the analyzer, they interfere with each other and create different colors depending on the amount of retardation.

In figure 2, the vertical lines represent the different wavelengths of light, with blue representing shorter wavelengths and red representing longer wavelengths. The colored bands represent the different amounts of retardation, with the blue band having the least amount of retardation and the red band having the most. As you correctly stated, when the two rays recombine at the analyzer, some wavelengths will be amplified (constructive interference) and some will be nullified (destructive interference). This results in the different colors seen on the chart.

The thickness of the sample also plays a role in the colors seen on the chart. Thicker samples will have a larger difference in retardation between the o-ray and the e-ray, resulting in a wider range of colors seen on the chart. Thinner samples will have a smaller difference in retardation, resulting in a narrower range of colors.