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How does anisotropy in liquid crystals affect the refraction of light?

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liquid crystal Figure 1: Arrangements of molecules.

The anisotropy of liquid crystals—their tendency to exhibit different physical properties depending on the direction of measurement—directly influences how they refract light, a phenomenon known as double refraction or birefringence.12

Because liquid crystals possess an ordered molecular structure, they are optically anisotropic. When unpolarized light enters this medium, the material's internal alignment causes the light to split into two distinct rays that travel at different speeds and in different directions.31

Ordinary ray: This ray experiences a constant refractive index regardless of the direction of travel.1
Extraordinary ray: This ray experiences a refractive index that varies based on its direction relative to the material's optic axis.1

This difference in refractive indices means the two rays travel at different speeds through the liquid crystal. Furthermore, because liquid crystals are sensitive to external influences, an electric field can be used to reorient the molecules, thereby altering the material's anisotropy and changing how it refracts light. This electro-optical effect is the fundamental principle behind the operation of liquid crystal displays.13