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• 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