Crystal Optics Uniaxial Crystal Optics A. Vibration Directions and R. I. - optic axis: single velocity - elsewhere: two mutually perpendicular components; Dh and Dl - vibration directions perpendicular to propatgation direction - one component travels with the same velocity in every direction through the crystal- O ray ordinary ray: r. i. is w. - other component is E ray or extraordinary ray: it travels with a velocity that depends on propagation direction within the Xtol. - E ray velocity = to that of o ray if light is propagated along the optic axis - E ray velocity most diff. fr. o ray velocity when propagation direction is perpendicular to optic axis. - r. i. associated with extreme valve of the E ray velocity is e. - w and e are the two principal r. i. for uniaxial crystals. - an infinite number of e values between (minimum) (e = w) and (maximum) (e). B. Indicatrix: geometric figure based on indices of refraction. - an ellipsoid of revolution (fig. 7-1): axis = 2e, direction of E ray when e is max; diameter is 2w, direction of O ray. - all but one of the sections through center of indicatrix are ellipses - one axis of every elliptical section has the same length, 2w;: r.i. is associated with one of the vib. directions in every line. X tol section is w. - one circular section of radius w: optic axis perpendicular to circular section. - velocities of O & E along o.a. are equal - called O; light not resolved into two unlike components not plane polorized; vib in all directions. - relation to crystallographic direction (fig. 7-3) - optic axis (rotation axis) is always the c axis, which coincides with e vibration direction for which e is a limit; light prop. perpendicular to c axis has r.i. e if it vibrates to c or ri.w. w if perpendicular to c. - optic sign: e may be w. axis of rotation e > w, positive (+) long (prolate e < w, negative (-) short (oblate C. Extinction - four times every 360 degrees for non-optic axis section (lining up of vib. directions N & S, E & W). - anisotropic grains remaining essentially dark upon rotation indicate an optic axis section. (Thus look for gray grains to obtain an optic axis section. - undulatory: each part of the grain extinguishes at a slightly different position –> effect is that of shadows crossing the grain. reason: due to slightly different orientations of vibration directions in different parts of the grain; exhibited by substances which have been physically deformed (strained) by , etc. - parallel = straight: when some extollographic direction (cleavage, crystal boundary) is parallel to a vibration direction (cancrinite). - symmetrical: when vibration direction bisects the between two cleavage directions (calcite). - inclined: cleavage inclined at any angle to a vibration direction (kyanite). - angle: between cleavage and extinction measured and recorded to aid in ID. Biaxial crystal optics - two optic axes along which light is propagated with the same velocity. - in every other direction - two plane-polarized components at 90 degrees have unequal velocity. - between optic axes is a useful variable related to sign. - three principal vibration directions and associated indices of refraction: x - - least y - - index of light prop. along an optic axis (analogous to w in uniaaxials) z - - greatest * A. Inticatrix: geometrical figure summarizing the vibration directions and r. I. (of all wave propogation directions.) - long axis of length (z), an intermed. axis at 90 degrees of length (y), and a short axis normal to the other two of length (x). - three symmetry planes: xy, xz, yz. - two circular sections and directions normal to these are optic axes. - any section of indicatrix (except two circular sections) is an ellipse whose axes show the directions of vibration of light prop. normal to that section; half-lengths of axes give r. i. All Pages Copyright © GeoClassroom. All Rights Reserved. 