  We used Geometric Algebra to compute the paths of skew rays in a cylindrical,
step-index multimode optical fiber. To do this, we used the vector addition
form for the law of propagation, the exponential of an imaginary vector form
for the law of refraction, and the juxtaposed vector product form for the law
of reflection. In particular, the exponential forms of the vector rotations
enables us to take advantage of the addition or subtraction of exponential
arguments of two rotated vectors in the derivation of the ray tracing
invariants in cylindrical and spherical coordinates. We showed that the light
rays inside the optical fiber trace a polygonal helical path characterized by
three invariants that relate successive reflections inside the fiber: the ray
path distance, the difference in axial distances, and the difference in the
azimuthal angles. We also rederived the known generalized formula for the
numerical aperture for skew rays, which simplifies to the standard form for
meridional rays.
