Behavior of extraordinary rays in uniaxial crystals

We have experimentally investigated the behavior of extraordinary rays (E rays) in uniaxial crystals for two cases: that in which optical axes are parallel to the surfaces and that in which they are inclined. The E ray always rotates around the ordinary ray (O ray) in the same direction that the crystal rotates around its surface normal. For the case when the axes are parallel to the surface, we discovered that the E ray rotates up to α = 2π as the crystal rotates to ? = π. The E ray traces a series of ellipses as the angle of incidence is varied. Snell's law is valid for the E ray only when the optical axes are perpendicular to the plane of incidence. For the case in which the optical axes are incident, the E ray and the crystal rotate at different speeds except for the case of normal incidence. The speed of rotation increases with the incidence angle. The ray traces a curve known as the Pascal worm, which is described by the equation (x(2) + z(2) - mx)(2) = n(2)(x(2) + z(2)). When the optical axes coincide with the plane of incidence, the space between the rays in the plane is not related to the angle of incidence.