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Why can light pass through crossed polarizers when a liquid crystal is placed between them?

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liquid crystal Figure 1: Arrangements of molecules.

When a liquid crystal is placed between crossed polarizers, light can pass through the assembly because the liquid crystal alters the polarization of the light as it travels through the material.1

In a twisted-nematic cell, the liquid crystal molecules are arranged in a twisted configuration between the two polarizers. As light passes through the first polarizer, it becomes polarized. As this light travels through the twisted layer of liquid crystal, the molecules guide the light's polarization, rotating it gradually by 90 degrees. By the time the light reaches the second polarizer, its polarization has been rotated to match the axis of the second filter, allowing it to pass through the assembly.23

If an electric field is applied, the liquid crystal molecules reorient, destroying the twisted structure. Without the twist to rotate the polarization, the light remains blocked by the second polarizer, causing the cell to appear dark.23