Is birefringence different in plastics, glass and calcite?

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Birefringence varies significantly across materials like plastics, tempered glass, and calcite crystals, producing distinct optical phenomena such as rainbow color bands in plastics, colorless checkerboard patterns in tempered glass, and double images in calcite. These differences are crucial for mineral identification in optical mineralogy, where birefringence and extinction angles help distinguish between minerals. The discussion also touches on stress-induced birefringence in materials like airplane cockpit windows, suggesting that color patterns may result from thin layer interference rather than birefringence alone. The underlying principles of birefringence are explained through Maxwell's equations, highlighting the relationship between the dielectric constant and refractive index in anisotropic materials. Understanding these concepts is essential for analyzing various materials in microscopy and geology.
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1) Is birefringence different in plastics, tempered glass and calcite crystal?

In plastics I see rainbow color bands (when looking through polaroid glasses), in tempered glass a colorless checkerboard pattern (again viewed through polaroid glasses), and in calcite double images. These different birefringence phenomena don't seem to occur together in materials, but I even could not find birefringence category names to distinguish them.

2) Is there a formula for the displacement of the extraordinary image relative to the ordinary image, in a calcite crystal?
 
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1) Is birefringence different in plastics, tempered glass and calcite crystal?

Yes I would expect it to be very different.
After all its different even between crystals of different minerals, say calcite, silia, mica
its one way to be able to distinguish different minerals when doing optical mineralogy ( Petrology)

here's an example of the mineral Epidote
attachment.php?attachmentid=59318&stc=1&d=1370477764.jpg


using birefringence, exticntion angle etc, determination of individual minerals within the sample can be done

When I was doing my geology degree, this was one area I really enjoyed. Grinding thin sections of minerals on microscope slides. Then doing the analysis of them with the microscope.regards
Dave
 

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In Wikipedia, this photo of an Airbus cockpit window is used as an illustration of stress induced birefringence. The color contours are assumed to correspond to tension lines because the left and right window colors are mirror images. However, the photo was taken without a polarizing filter on the camera, so there is some doubt that birefringence is involved here. What else could explain these color contours?

640px-LHcockpitWindow.jpg
 
The colors may be due to thin layer interference.
Maybe in the inner layer of polymer.
The tension in the window may change the thickness of the layer a little so the colors may indeed be a map of the stress. Only the mechanism is a little different.

A similar effect can be seen when you press together two microscope slides. The pattern of interference colors changes when you squeeze the "sandwich" with your fingers. But in this case there is just air between the slides. I don't know what is the airplane windshield structure but is very likely to be a multiple layer structure.
 
Isn't there a formula for the displacement of the extraordinary image relative to the ordinary image, in a calcite crystal?
 
"The phenomenon of double refraction is based on the laws of electromagnetism, first proposed by British mathematician James Clerk Maxwell in the 1860s. His elaborate series of equations demonstrate that the velocity of light through a material equals the speed of light in a vacuum (c) divided by the product of the square root of the material's dielectric constant (e) multiplied by the magnetic permeability (m) of the medium. In general, biological and related materials have a magnetic permeability very near 1.0, as do many conducting and non-conducting specimens of interest to the microscopist. The dielectric constant of a material is therefore related to the refractive index through a simple equation:
ε = n2
where e is a variable representing the dielectric constant, and n is the material's measured refractive index. This equation was derived for specific frequencies of light and ignores dispersion of polychromatic light as it passes through the material. Anisotropic crystals are composed of complex molecular and atomic lattice orientations that have varying electrical properties depending upon the direction from which they are being probed. As a result, the refractive index also varies with direction when light passes through an anisotropic crystal, giving rise to direction-specific trajectories and velocities."

http://www.microscopyu.com/articles/polarized/birefringenceintro.html
 
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Imagine a charged sphere at the origin connected through an open switch to a vertical grounded wire. We wish to find an expression for the horizontal component of the electric field at a distance ##\mathbf{r}## from the sphere as it discharges. By using the Lorenz gauge condition: $$\nabla \cdot \mathbf{A} + \frac{1}{c^2}\frac{\partial \phi}{\partial t}=0\tag{1}$$ we find the following retarded solutions to the Maxwell equations If we assume that...
Maxwell’s equations imply the following wave equation for the electric field $$\nabla^2\mathbf{E}-\frac{1}{c^2}\frac{\partial^2\mathbf{E}}{\partial t^2} = \frac{1}{\varepsilon_0}\nabla\rho+\mu_0\frac{\partial\mathbf J}{\partial t}.\tag{1}$$ I wonder if eqn.##(1)## can be split into the following transverse part $$\nabla^2\mathbf{E}_T-\frac{1}{c^2}\frac{\partial^2\mathbf{E}_T}{\partial t^2} = \mu_0\frac{\partial\mathbf{J}_T}{\partial t}\tag{2}$$ and longitudinal part...

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