  We consider light propagation through a twisted nematic liquid crystal. At
first, an expression for light transmission is obtained using a rather
intuitive approach. Secondly, an accurate solution for light transmission based
on Maxwell's equations is derived and compared with the previous one. Both
approaches show that when changes in the orientation of the liquid crystal
optical axis are small on the scale defined by the optical wavelength (Mauguin
limit), the polarization of light approximately follows the optical axis. At
the same time, even in this limit, the simple formula for the light
transmittance mentioned in some monographs on liquid crystal displays is not
necessary accurate. Conditions under which the two approaches give the same
expression for the light transmission are found. In addition, two numerical
methods for finding the light transmittance are considered. It is demonstrated
that the Gauss-Seidel method has much faster convergence rate than the Euler
method.
