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 = hn f /c Slow ray takes t = hn s /c Time lag = Δt = hn s /c - hn f /c = h(n s – n f )/c Fast ray leads slow ray by c Δt = h(n s – n f ) This quantity is called retardation The quantity n s – n f 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 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
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 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.
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 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