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When light is passed through an isotropic liquid it only experiences one refractive index - therefore polarised light entering the sample retains the same polarisation upon exiting it.

The result, when viewed through crossed polars, is complete darkness as all of the light passing through the material is absorbed by the analyser.
However if the substance is anisotropic then the light experiences more than one refractive index.

(In the case of a liquid crystal, with the optic axis along the director different to the others, there are two refractive indices n1 and n2).
When the two components of the light recombine at the other end of the liquid crystal the resulting beam now has a new polarisation to the one that entered the sample.

The rotation of the polarisation plane means that in most cases light exiting the liquid crystal is no longer polarised perpendicular to the analyser. This means that at least some component of it can pass through and is now seen by the observer.
The exception is when the optical path difference is equal to a multiple of the wavelength of the light passing through it.

In this case the plane of polarisation is rotated 360° (i.e. it is unchanged) upon exiting the liquid crystal and so the analyser, as before, blocks this particular wavelength.