  In light refraction between two transparent media, Snell's law describes the
relationship between the incident angle and refraction angle. The refractive
index is usually determined from Snell's law using the minimum deviation angle
through a prism. A medium that partially absorbs light has complex permittivity
(or permeability), and its refractive index has an imaginary part. Because of
the imaginary part, Snell's law does not hold for light-absorbing media.
Accordingly, other methods is required to determine the complex value of the
refractive index in a light-absorbing medium. The exact solution of Maxwell's
equations was obtained for light passing through a prism composed of a
light-absorbing medium. Thereby the optical path was determined. The difference
of optical paths between light-absorbing medium and transparent medium was
calculated numerically. The difference is very large in the neighborhood of
perfect reflection area of transparent medium. We found two methods to
determine the complex value of the refractive index using the optical path.
Both methods analyzed the solutions in detail for two specific incident angles.
The deviation angles corresponding to the two incident angles determined the
complex value of the prism's refractive index. The obtained refractive index is
independent of the apex angle of the prism.
