Refractive index • N ~ 1/(velocity of light) Optical Mineralogy • Snell’s law n = sin i / sin r • Mineral relief A short review – Negative, low, medium high compared with surroundings • Becke fringe – Bright halo moved toward material of higher n when viewing distance is increased Mineral Relief Indicatrix • Negative relief • The 3-D figure defined by the minerals – Alkali feldspars, feldspathoids refractive index • Low relief • Isotropic –Quartz – The indicatrix is a sphere and there is only one • Moderate relief index of refraction – Mafic minerals, apatite • Anisotropic • High relief – The indicatrix is an ellipsoid and there are two – Zircon, calcite, garnet or three mutually perpendicular indices Double Refraction Uniaxial Crystals • Anisotropic minerals exhibit double • Have two principal R.I. Termed ordinary refraction for most grain orientations (O) and extraordinary (E) • Double refraction causes interference • Hexagonal and tetragonal minerals are coloration under polarized light uniaxial (i.e. quartz and apatite) • The strength of double refraction is termed • Indicatrix is an ellipsoid of revolution birefringence • The maximum birefringence is a means to • O vibrates perpendicular to c axis characterize minerals • E vibrates parallel to the c axis 1 • Circular Section –(⊥ optic axis: all ω's) Fig. 6-12 Uniaxial Indicatrix • Principal Sections – (have ω and true ε: max & min n's) • Optically positive is prolate (elongate to c) • Random Sections (ε' and ω) –O fast – always have ω!! – Quartz example • Optically negative is oblate (flattened to c) Any cut through center of a –O slow uniaxial indicatrix will have ω as – Apatite example one semiaxis Biaxial Indicatrix Ordinary Light Observations • Three mutually perpendicular principal • Crystal form indices, n , n , and n X Y Z • Cleavage • X is the fast vibration direction – lowest refractive index • Refraction relief • Y is the intermediate vibration direction • Becke fringe • Z is the slow vibration direction – Highest refractive index • Mineral color Pleochroism Crossed-Polar Observations • The dependence of color on orientation in • Extinction angles polarized light – Relation of X, Y, and Z to • Some minerals have distinctive colors crystallography depending on their orientation when viewed in plane polarized light • Birefringence – Hornblende and Biotite have strong – Maximum difference (nZ –nX) pleochrosim – Hypersthene has weak pleochroism 2 Extinction Extinction Angle • A mineral appears extinct (dark) if its vibration • The angle measured between an extinction direction is parallel to the polarize under x- position and a prominent crystal direction polarized light • For uniaxial minerals there is parallel • This is the case for: extinction to the c axis – Isotropic materials in any orientation • For orthorhombic minerals there is parallel – Uniaxial minerals perpendicular to c axis extinction to the three crystallographic axes – Biaxial minerals perpendicular to optic axis • Monoclinic and triclinic minerals have • Other orientations exhibit birefringence inclined extinction Birefringence Measuring Birefringence • Other than isotropic materials and minerals • Choose a grain with maximum oriented perpendicular to optic axis, the interference colors trace of two different indices lie in the plane of the thin section • Rotate 45° from extinction • The difference (n –n ) is the birefringence Z X • Match the mineral colors with a chart • The apparent birefringence (nZ’ – nX’) is generally seen • Only a few grains will show true (nZ –nX) Birefringence for I.D. • Minerals may be classed as: low, moderate, high, and very high birefringence •Low: 1st order – quartz, apatite • Moderate: 2nd order – Augite •High 3rd order – Biotite • Very high – Carbonates, sphene 3.