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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.

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