Optical Dispersion

Optical dispersion is the variation of optical properties with wavelength of light. Just as isotropic minerals have a slightly different index of refraction for each wavelength of visible light (normal dispersion), biaxial minerals have different values of nα, nβ, and nγ for each wavelength. Because the optic angle 2V depends on these three principal indices, its value also varies with wavelength - this is optic axis dispersion. When the dispersion is strong enough, visible color fringes appear along the isogyres in interference figures, making dispersion a diagnostic microscopic property. ^[1]

Optic Axis Dispersion

Optic axis dispersion refers specifically to variation in the size of 2V with wavelength. The orientation of the indicatrix axes relative to the crystal axes stays fixed, but the angle between the two optic axes is different for red light than for violet light. The convention for reporting this is straightforward: if 2V for red light is larger than 2V for violet light, the dispersion is described as r > v. If 2V for violet light is larger, it is described as v > r. ^[1]

The color fringes arise because the isogyres for red and violet light do not coincide. The isogyre for violet light marks the area where no violet light passes; the isogyre for red light marks where no red light passes. A red fringe therefore appears where the melatopes for violet light are located - because violet is absent there, the remaining colors combine as red. A blue fringe appears where the melatopes for red light are located. Where the two isogyres overlap, a normal dark isogyre is seen. Dispersion is described qualitatively as weak, moderate, or strong, depending on how visible these colored fringes are in the interference figure. ^[1]

Orthorhombic minerals can display only optic axis dispersion. Their indicatrix axes are symmetry-constrained to be parallel to the crystallographic axes and cannot rotate - the indicatrix orientation is identical for all wavelengths. Only the size of 2V is free to vary with wavelength. ^[1]

Indicatrix (Bisectrix) Dispersion

Indicatrix dispersion, also called bisectrix dispersion, is the variation of the indicatrix orientation - not just 2V - with wavelength. Because monoclinic minerals have only one symmetry-fixed indicatrix axis (one axis must coincide with b), the other two indicatrix axes are free to rotate within the {010} plane as wavelength changes. Triclinic minerals have no fixed indicatrix axis at all, so all three can vary freely. Indicatrix dispersion is therefore exclusive to monoclinic and triclinic minerals. ^[1]

For monoclinic minerals, three types of indicatrix dispersion are possible, determined by which indicatrix axis coincides with the b crystallographic axis: ^[1]

Inclined Dispersion

Inclined dispersion is produced when the optic normal (Y) is parallel to the b axis. Because Y is fixed for all wavelengths, the optic plane (XZ) is also fixed - the {010} plane is the optic plane for every color. However, the X and Z axes are free to rotate within the {010} plane as wavelength changes, so 2V varies. The result is that color fringes in the acute bisectrix figure are symmetrical across the trace of the optic plane. ^[1]

Horizontal (Parallel) Dispersion

Horizontal dispersion (also called parallel dispersion) is produced when the obtuse bisectrix (Bxo) is parallel to the b axis. In this case the b axis is fixed for all wavelengths, but the optic plane pivots about b. This means the position of the Bxa for red light emerges at a different point within the {010} plane than the Bxa for violet light. Color fringes in the acute bisectrix figure are symmetrical across the trace of the optic normal rather than across the optic plane. ^[1]

Crossed Bisectrix Dispersion

Crossed bisectrix dispersion is produced when the acute bisectrix (Bxa) itself is parallel to b. The optic plane pivots about the Bxa as wavelength changes. Because the b axis is vertical in an acute bisectrix figure (Bxa is perpendicular to the stage), the color fringes are symmetrical by 2-fold rotation about the Bxa rather than about any single line. ^[1]

The three types of monoclinic dispersion are diagnostic: the symmetry of the color fringe pattern in the interference figure directly reveals which indicatrix axis coincides with b, which can then be compared with published optic orientations to aid mineral identification. In practice, dispersion is most noticeable in minerals with large 2V variation across the visible spectrum, and its detection requires that the isogyres be clearly resolved - this is easiest in minerals with moderate to high birefringence and relatively few isochromes.

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