LOCATION OF RAY PATHS FOR A KNOWN WAVE NORMAL IN BIAXIAL CRYSTALS

The values of the principal indices of refraction determine the proper ties of the optical indicatrix. The directions of the ray paths associ ated with a wave normal ultimately depend on the indices of refraction . The directions of the wave normal and ray paths need not coincide in anisotropic media. To find a ray path for a given wave normal, two it ems of information must be extracted from the properties of the indica trix: the location of a vector representing a vibration direction or e lectric displacement vector, D, and the direction of the vector repres enting the electric field generated by the electromagnetic radiation, E. The angle 2V and optic sign, obtainable from the indices of refract ion, are all the information needed to calculate vectors parallel to t he vibration directions associated with a given wave normal. A second- rank tensor, with principal components inversely proportional to the s quares of the principal indices of refraction of the crystal, relates vectors representing the vibration direction and the electric field, D and E. E is calculated from this relation. The angle between D and E equals the angle between the wave normal and the ray path. Maximum val ues of the angles between ray path and wave normal depend on the large st index of refraction, gamma, and the birefringence of the crystal (g amma - alpha). For common rock-forming minerals, the maximum angle is approximately 0.5 degrees - 2 degrees. In crystals with extreme birefr ingence, such as aragonite and strontianite, the maximum angle approac hes 6 degrees. Wave normals and ray paths diverge most in sections cut parallel to the Y vibration direction and tilted with their normals b etween 45 degrees and 50 degrees from the Z vibration direction. The p recise angle between the Z vibration direction and the normal to the s ection depends on gamma and (gamma - alpha).