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We consider light propagation through a twisted nematic liquid crystal. Atfirst, an expression for light transmission is obtained using a ratherintuitive approach. Secondly, an accurate solution for light transmission basedon Maxwell's equations is derived and compared with the previous one. Bothapproaches show that when changes in the orientation of the liquid crystaloptical axis are small on the scale defined by the optical wavelength (Mauguinlimit), the polarization of light approximately follows the optical axis. Atthe same time, even in this limit, the simple formula for the lighttransmittance mentioned in some monographs on liquid crystal displays is notnecessary accurate. Conditions under which the two approaches give the sameexpression for the light transmission are found. In addition, two numericalmethods for finding the light transmittance are considered. It is demonstratedthat the Gauss-Seidel method has much faster convergence rate than the Eulermethod.

Computational physics approaches to light transmission through a twisted nematic liquid crystal slab