LOCAf,ION OF RAY PATHS FOR A KNOWN WAVE NORMAL IN BIAXIAL CRYSTALS

The values of the principal indices of reftaction determine the properties of the optical indicatrix. The directions of the ray paths associaGd with a wave normal ultimately alepend 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 ofthe indicatrix: the location ofa vector representing a vibration direction or electric displacement vector, D, and the direction of the vector representing the electric fleld generated by the electromagnetic radiation, E. The angle 2V and optic sign, obainable 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 invenely proportional to the squares of the principal indices of refuaction of the crystal, relales vectors representing the vibration direction and the electric fie14 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, 1, and the birefringence of the crystal (y o). For common rock-forming minerals, the maximum angle is approximately 0.5o 2o. In crystals with extreme birefringence, such as aragonite and strontianit€, the maximum angle approaches 6o. Wave nomrals and ray paths diverge most in sections cut parallel to the I vibration direction and tilted with their normals between 45o and 50o from the Z vibration direction. The precise angle between the Z vibration direction and the normal to the section depends on 1 and (1cr).