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Is birefringence different in plastics, glass and calcite?

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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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