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Mineralogy · Problem type

Isotropic or anisotropic under crossed polars

Use this for “A grain stays dark under crossed polars as the stage turns. Could it be quartz, or is it garnet?”

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Under crossed polars, is it isotropic or anisotropic?
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Cubic minerals and glass have one refractive index, so crossed polars stay dark.

Assumptions

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Crossed polars: the lower polarizer and the upper analyzer are at 90°, so no light passes through an empty slide.
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Light crosses a cubic mineral or a glass at one speed in every direction.
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Every other crystal system splits light into two rays, so grains show colors and go dark only four times a turn.
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