The transmission and reflection of a monochromatic electromagnetic wav
e in a twisted nematic wedge are investigated. We consider the special
case where the characteristic length xi of the director twist is much
higher than the optical wavelength lambda. By using the perturbative
theoretical procedure proposed by Oldano et al., we find an analytic e
xpression for the transmitted and reflected beams at the first order i
n the perturbative parameter epsilon = 1/Delta k xi, where Delta k is
the difference between the extraordinary and ordinary wavenumbers. The
intensity and the polarization of the refracted and reflected beams a
re related by simple analytic expressions to the normal derivatives of
the director at the interfaces and do not depend on details of the bu
lk director distortion. The theoretical predictions are compared with
experimental results obtained using an electric field to twist the dir
ector-field A satisfactory agreement is found between theory and exper
iment. On the basis of our theoretical results we propose a simple exp
erimental method to measure the twist viscosity coefficient of nematic
liquid crystals.