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 = nλ
Retardation = (n+1/2)λ
Retardation
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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
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 direction
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
• 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 Indicatrix
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)
The Indicatrix
The Indicatrix and What You See
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.
Optic Axes
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 Viewing
Conoscopic Viewing
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
Uniaxial Interference Figure
Uniaxial Interference Figure
Biaxial Isochromes
Biaxial Isogyres
Biaxial Interference Figure
Biaxial Interference Figure