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How can polarized light produce colours when it passes through certain crystals?

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A circular RYB color wheel divided into twelve segments, showing a progression of colors from red, orange, and yellow to green, blue, and violet. — colour The RYB color model is being illustrated on a color wheel.

Polarized light produces colours when passing through certain crystals primarily through the interaction of birefringence and interference.

When polarized white light enters a doubly refracting (birefringent) material, the crystal splits the light into two components that vibrate in mutually perpendicular planes. Because the refractive index of the crystal varies depending on the direction of vibration, these two components travel through the material at different speeds.12

As these rays emerge from the crystal, they possess a phase difference—a result of the difference in their travel times—which allows them to interfere with one another. When this light is viewed through a second polarizing filter (an analyzer), specific wavelengths are reinforced or canceled out depending on the thickness of the crystal and the orientation of the light's vibration. This selective cancellation and reinforcement of wavelengths creates the visible colours observed in the material. This phenomenon is widely used in science to analyze the mineral composition of rocks or to detect stress in structural materials.342