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

JAMES NICHOLLS
Department of Geology and Geophysics, University of Calgary, Calgary, Alberta T2N 1N4

Abstract

The values of the principal indices of refraction determine the properties of the optical indicatrix. The directions of the ray paths associated 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 items of information must be extracted from the properties of the indicatrix: the location of a vector representing a vibration direction or electric displacement vector, D, and the direction of the vector representing the electric field generated by the electromagnetic radiation, E. The angle 2V and optic sign, obtainable from the indices of refraction, are all the information needed to calculate vectors parallel to the vibration directions associated with a given wave normal. A second-rank tensor, with principal components inversely proportional to the squares 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 values of the angles between ray path and wave normal depend on the largest index of refraction, , and the birefringence of the crystal ( - ). For common rock-forming minerals, the maximum angle is approximately 0.5 - 2 . In crystals with extreme birefringence, such as aragonite and strontianite, the maximum angle approaches 6 . Wave normals and ray paths diverge most in sections cut parallel to the Y vibration direction and tilted with their normals between 45 and 50 from the Z vibration direction. The precise angle between the Z vibration direction and the normal to the section depends on and ( - ).