Presentation on theme: "Light ray overview Rays are split into 2 orthogonal rays (e and w) – these rays are slowed to different degrees (apparent birefringence, d related to the."— Presentation transcript:
1 Light ray overviewRays are split into 2 orthogonal rays (e and w) – these rays are slowed to different degrees (apparent birefringence, d related to the refractive index, n; d=ne-nw), and can go in different directions, resulting in a different length to get through a mineral (retardation, D, which is a function of both birefringence and thickness of the mineral)
2 When the rays exit the crystal they recombine Polarized light going into the crystal splits into two rays, going at different velocitiesone is O-ray with n = wother is E-ray with n = eWhen the rays exit the crystal they recombineWhen rays of different wavelengthcombine what things happen?ewpolarizer
6 Color can be quantified numerically: d = nhigh - nlow Colors one observes when polars are crossed (XPL)Color can be quantified numerically: d = nhigh - nlow
7 Rotation of crystal? Retardation also affected by mineral orientation! As you rotate a crystal, observed birefringence colors changeFind maximum interference color for each in practice
8 ExtinctionWhen you rotate the stage extinction relative to the cleavage or principle direction of elongation is extinction angleParallel, inclined, symmetric extinctionDivided into 2 signs of elongation based on the use of an accessory plate made of gypsum or quartz (which has a retardation of 550 nm) which changes the color for a grain at 45º from extinction look for yellow (fast) or blue (slow)
9 Time for some new tricks: the optical indicatrix Thought 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?
10 Isotropic indicatrixLight travels the same distance in all directions;n is same everywhere, thus d = nhi-nlo = 0 = blackSoccer ball(or an orange)
12 Uniaxial indicatrixCircular section is perpendicular to the stem (c-axis)
13 Propagate light along the c-axis, note what happens to it in plane of thin section nw - nw = 0therefore, d=0: grain stays black(same as the isotropic case)nw
14 This orientation will show the maximum d of the mineral Now propagate light perpendicular to c-axisNSWEne - nw > 0therefore, d > 0nenwnenwnenwnenwnenwGrain changes color upon rotation. Grain will go black whenever indicatrix axis is E-W or N-SThis orientation will show the maximum d of the mineral
15 Biaxial indicatrix (triaxial ellipsoid) The potato!2VzThere are 2 different ways to cut this and get a circle…
16 Alas, the potato (indicatrix) can have any orientation within a biaxial mineral… augiteolivine
17 anisotropic minerals - biaxial indicatrix feldsparclinopyroxeneNow things get a lot more complicated…
18 anisotropic minerals - uniaxial indicatrix c-axisLet’s perform the same thought experiment…c-axiscalcitequartz
19 Uniaxial indicatrix (biaxial ellipsoid) What can the indicatrix tell us about optical properties of individual grains?
20 2V: a diagnostic property of biaxial minerals When 2V is acute about Z: (+)When 2V is acute about X: (-)When 2V=90°, sign is indeterminateWhen 2V=0°, mineral is uniaxial2V is measured using an interference figure…More in a few minutes
21 Conoscopic 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 ortho® Interference Figures Very useful for determining optical properties of xlFig 7-13 Bloss, Optical Crystallography, MSA
23 Uniaxial Interference Figure O EUniaxial Interference FigureCircles of isochromesBlack cross (isogyres) results from locus of extinction directionsCenter of cross (melatope) represents optic axisApprox 30o inclination of OA will put it at margin of field of viewFig. 7-14
24 Uniaxial FigureCentered axis figure as 7-14: when rotate stage cross does not rotateOff center: cross still E-W and N-S, but melatope rotates around centerMelatope outside field: bars sweep through, but always N-S or E-W at centerFlash Figure: OA in plane of stage Diffuse black fills field brief time as rotateFig. 7-14
25 Optic Sign Find NE-SW quadrants of the field Slide the full wave (550nm) plate (aka gypusm plate) inThis slows the ray aligned NE-SW relative to the retardation - if that ray is more retarded it turns blue (adds 550 nm of retardation)
26 Biaxial Minerals – Optic Axes Biaxial Minerals have 2 optic axesRecall 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, birefringenceThe 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 -)
27 … but there are a few generalizations that we can make The potato has 3 perpendicular principal axes of different length – thus, we need 3 different RIs to describe a biaxial mineralX direction = na (lowest)Y direction = nb (intermed; radius of circ. section)Z direction = ng (highest)Orthorhombic: axes of indicatrix coincide w/ xtl axesMonoclinic: Y axis coincides w/ one xtl axisTriclinic: none of the indicatrix axes coincide w/ xtl axes
28 Biaxial interference figures There 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 sign w/ gyps(+)(-)determine 2V from curvature of isogyre90°60°40°
29 Biaxial interference figures 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 d.Use this figure to get sign and 2V:2V=20°2V=40°2V=60°(+)
30 Isotropic? Uniaxial? Biaxial? Sign? 2V? Quick 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 sectionhi dlo dIsotropic? Uniaxial? Biaxial? Sign? 2V?All of these help us to uniquely identify unknown minerals.
31 Review – techniques for identifying unknown minerals Start in PPL:Color/pleochroismReliefCleavagesHabitThen go to XPL:BirefringenceTwinningExtinction angleAnd Confocal lense:Uniaxial or biaxial?2V if biaxialPositive or negative?
32 Go to your book… Chemical formula Symmetry Uniaxial or biaxial, (+) or (-)RIs: lengths of indicatrix axesBirefringence (d) = N-n2V if biaxialDiagrams:Crystallographic axesIndicatrix axesOptic axesCleavagesExtinction angles