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Polarized Light. Polarized Light. Polarizing Filters. Natural Polarization. Double Refraction. Polarized Light in Crystals. Privileged Directions. Fast and Slow Directions. Fast and Slow Rays. Retardation. Retardation = n λ. Retardation = (n+1/2) λ. Retardation.

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Retardation1
Retardation

  • One ray is fast, one slow

  • v = c/n (n = index of refraction)

  • Time to traverse thin section = h/v = hn/c

  • Fast ray takes t = hnf/c

  • Slow ray takes t = hns/c

  • Time lag = Δt = hns/c - hnf/c = h(ns – nf)/c

  • Fast ray leads slow ray by c Δt = h(ns – nf)

  • This quantity is called retardation

  • The quantity ns – nf is called birefringence


Retardation2
Retardation

  • If the retardation = integer number of wavelengths, light recombines with no change, and is blocked

  • If the retardation = integer number of wavelengths plus 1/2, light recombines perpendicular to its original direction, and is fully transmitted

  • Materials with zero birefringence (isometric or noncrystalline) are called isotropic



Vibration direction1
Vibration Direction

  • The optical properties of a mineral are determined by vibration direction

  • The ray path has little role

  • We have to look at light differently


The indicatrix
The Indicatrix

  • How can we summarize optical behavior in all directions?

  • The indicatrix is an ellipsoid with radius equal to refractive index for that vibration direction.

  • Shape of the indicatrix reflects symmetry of crystal



The indicatrix2
The Indicatrix

  • Isometric or noncrystalline materials have the same RI in all directions (isotropic). The indicatrix is a sphere.

  • Hexagonal, trigonal and tetragonal minerals have one high symmetry axis (uniaxial). The indicatrix is an ellipsoid of revolution

  • All other minerals have an indicatrix with 3 unequal axes (biaxial)




Optic axes
Optic Axes

  • If RI doesn’t vary, there is no retardation and no interference color.

  • This happens if cross section of indicatrix is a circle.

  • Every mineral has at least one circular cross section.

  • Direction perpendicular to a circular cross section is called an optic axis.



What optical behavior
What Optical Behavior?

  • Isotropic minerals are easy – they never show interference colors

  • Can we somehow see the optical behavior in many directions at once?

    • If we could turn a grain at will, that would be great

    • Universal stages are expensive and laborious to use

    • Can we send light through in many different directions at once and see what happens?




Conoscopic observation
Conoscopic Observation

  • Retardation increases away from optic axis

    • Higher birefringence

    • Greater thickness of material

    • We see concentric color bands (isochromes)

  • Some areas of the field go extinct

    • Extinction areas are called isogyres








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