Time for some new tricks: the optical indicatrixThought experiment:Consider an isotropic mineral (e.g., garnet)Imagine point source of light at garnet center; turn light on for fixed amount of time, then map out distance traveled by light in that timeWhat geometric shape is defined by mapped light rays?Isotropic indicatrixSoccer ball(or an orange)Light travels the same distance in all directions;n is same everywhere, thus = nhi-nlo= 0 = blackanisotropic minerals - uniaxial indicatrixquartzcalcitec-axisc-axisLet’s perform the same thought experiment…Uniaxial indicatrixc-axisc-axisSpaghetti squash = uniaxial (+)tangerine = uniaxial (-)quartzcalciteCircular section is perpendicular to the stem (c-axis)Uniaxial indicatrixUniaxial indicatrix(biaxial ellipsoid)nna=Xc=Zb=Yna=Xc=Znb=YWhat can the indicatrix tell us about optical properties of individual grains?n - n = 0therefore, =0: grain stays black (same as the isotropic case)nna=Xc=Zb=YnnPropagate light along the c-axis, note what happens to it in plane of thin sectionGrain changes color upon rotation.Grain will go black whenever indicatrix axis is E-W or N-S nnThis orientation will show the maximum of the mineralnnn - n > 0therefore, > 0NSW ENow propagate light perpendicular to c-axisConoscopic ViewingA condensing lens below the stage and a Bertrand lens above itArrangement essentially folds planes coneLight rays are refracted by condensing lens & pass through crystal in different directionsThus different propertiesOnly light in the center of field of view is vertical & like orthoInterference Figures Very useful for determining optical properties of xlFig 7-13 Bloss, Optical Crystallography, MSAHow interference figures work (uniaxial example)BertrandlensSample(looking down OA)sub-stagecondenserW E-W polarizerN-S polarizerWhat do we see??© Jane Selverstone, University of New Mexico, 2003Interference figure provides a zoomed ‘picture’ of the optic axes and the areas around that which have rays which are split and refracted – must be gathered in line with optic axis!!Uniaxial Interference FigureFig. 7-14O E• Circles of isochromes• Black cross (isogyres) results from locus of extinction directions• Center of cross (melatope) represents optic axis• Approx 30oinclination of OA will put it at margin of field of viewUniaxial Figure– Centered axis figure as 7-14: when rotate stage cross does not rotate– Off center: cross still E-W and N-S, but melatope rotates around center– Melatope outside field: bars sweep through, but always N-S or E-W at center– Flash Figure: OA in plane of stage Diffuse black fills field brief time as rotateFig. 7-14Optic Sign• Find NE-SW quadrants of the field• Slide the full wave (550nm) plate (aka gypusm plate) in• This slows the ray aligned NE-SW relative to the retardation - if that ray is more retarded it turns blue (adds 550 nm of retardation)anisotropic minerals - biaxial indicatrixclinopyroxenefeldsparNow things get a lot more complicated…Biaxial indicatrix(triaxial ellipsoid)OAOA2VzYXZnnnnnnnnnnnThe potato!2VzThere are 2 different ways to cut this and get a circle…Alas, the potato (indicatrix) can have any orientation within a biaxial mineral…cabZXYYaZbXcolivineaugiteBiaxial Minerals – Optic Axes• Biaxial Minerals have 2 optic axes– Recall that biaxial minerals are of lower symmetry crystal classes (orthorhombic, monoclinic, and triclinic)• The plane containing the 2 optic axes is the optic plane  looking down either results in extinction in XPL-no retardation, birefringence• The acute angle between the 2 different optic axes is the 2V angle  how this angle relates to the velocities of refracted rays in the crystal determines the sign (+ or -)… but there are a few generalizations that we can makeThe potato has 3 perpendicular principal axes of different length – thus, we need 3 different RIs to describe a biaxial mineralX direction = n (lowest)Y direction = n (intermed; radius of circ. section)Z direction = n (highest)• Orthorhombic: axes of indicatrix coincide w/ xtl axes• Monoclinic: Y axis coincides w/ one xtl axis• Triclinic: none of the indicatrix axes coincide w/ xtl axesOAOA2VzYXZnnn2V: a diagnostic property of biaxial minerals• When 2V is acute about Z: (+)• When 2V is acute about X: (-)• When 2V=90°, sign is indeterminate• When 2V=0°, mineral is uniaxial2V is measured using an interference figure… More in a few minutesBiaxial interference figuresThere are lots of types of biaxial figures… we’ll concentrate on only two1. Optic axis figure - pick a grain that stays dark on rotationWill see one curved isogyredetermine 2V from curvature of isogyre90° 60° 40°determine sign w/ gyps(+) (-)2. Bxa figure (acute bisectrix) - obtained when you are looking straight down between the two O.A.s. Hard to find, but look for a grain with intermediate .Biaxial interference figuresUse this figure to get sign and 2V:(+)2V=20° 2V=40° 2V=60°OAOA2VzYXZnnnQuick review:Indicatrix gives us a way to relate optical phenomena to crystallographic orientation, and to explain differences between grains of the same mineral in thin sectionOAOA2VzYXZnnnhi OAOA2VzYXZnnnlo Isotropic? Uniaxial? Biaxial? Sign? 2V?All of these help us to uniquely identify unknown minerals.Review – techniques for identifying unknown mineralsStart in PPL:• Color/pleochroism• Relief• Cleavages• HabitThen go to XPL:• Birefringence• Twinning• Extinction angleAnd Confocal lense:• Uniaxial or biaxial?• 2V if biaxial• Positive or negative?Go to your book…• Chemical formula• Symmetry• Uniaxial or biaxial, (+) or (-)• RIs: lengths of indicatrix axes• Birefringence ( ) = N-n• 2V if biaxialDiagrams:* Crystallographic axes* Indicatrix axes* Optic axes* Cleavages* Extinction