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UVM GEOL 135 - Lecture 9 - Optics II

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Light ray overviewSlide 2Michel-Lévy Color Chart – Plate 4.11Slide 4Slide 5Slide 6Rotation of crystal?ExtinctionSlide 9Slide 10Slide 11Slide 12Slide 13Slide 14Biaxial indicatrix (triaxial ellipsoid)Slide 16Slide 17Slide 18Uniaxial indicatrix (biaxial ellipsoid)Slide 20Conoscopic ViewingSlide 22Uniaxial Interference FigureUniaxial FigureOptic SignBiaxial Minerals – Optic AxesSlide 27Slide 28Slide 29Slide 30Slide 31Slide 32Light ray overview•Rays are split into 2 orthogonal rays ( and ) – these rays are slowed to different degrees (apparent birefringence, related to the refractive index, n; =n-n), and can go in different directions, resulting in a different length to get through a mineral (retardation, , which is a function of both birefringence and thickness of the mineral)Polarized light going into the crystal splits  into two rays, going at different velocitiesone is O-ray with n = other is E-ray with n = When the rays exit the crystal they recombinerecombineWhen rays of different wavelength combine  what things happen?polarizerMichel-Lévy Color Chart – Plate 4.11Example: Quartz  = 1.544  = 1.5531.5531.544Data from Deer et al Rock Forming MineralsJohn Wiley & SonsWhat interference color is this?What interference color is this?Colors one observes when polars are crossed (XPL) Color can be quantified numerically:  = nhigh - nlowRotation of crystal?•Retardation also affected by mineral orientation!•As you rotate a crystal, observed birefringence colors change•Find maximum interference color for each in practiceExtinction•When you rotate the stage  extinction relative to the cleavage or principle direction of elongation is extinction angle•Parallel, inclined, symmetric extinction•Divided 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)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 = blackUniaxial indicatrixc-axisc-axisSpaghetti squash = uniaxial (+)tangerine = uniaxial (-)quartzcalciteCircular section is perpendicular to the stem (c-axis)Uniaxial indicatrixn - n = 0therefore, =0: grain stays black (same as the isotropic case) nna=Xc=Zb=YnnPropagate 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 nnThis orientation will show the maximum  of the mineralnnnnnnnnn - n > 0therefore, > 0NSW ENow propagate light perpendicular to c-axisBiaxial indicatrix(triaxial ellipsoid)OAOA2VzYXZnnnnnnnnnnnThe 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…cabZXYYaZbXcolivineaugiteanisotropic minerals - biaxial indicatrixclinopyroxenefeldsparNow things get a lot more complicated…anisotropic minerals - uniaxial indicatrixquartzcalcitec-axisc-axisLet’s perform the same thought experiment…Uniaxial indicatrix(biaxial ellipsoid)nna=Xc=Zb=Yna=Xc=Znb=YWhat can the indicatrix tell us about optical properties of individual grains?OAOA2VzYXZnnn2V: 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 minutesConoscopic ViewingConoscopic ViewingA condensing lencondensing lens below the stage and a Bertrand lensBertrand 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 FiguresInterference Figures Very useful for determining optical properties of xlFig 7-13 Bloss, Optical Crystallography, MSAHow interference figures work (uniaxial example)How interference figures work (uniaxial example)BertrandlensSample(looking down OA)sub-stagecondenserW E-W polarizerN-S polarizerWhat do we see??What do we see??nnnnnnnn© 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 Uniaxial Interference FigureFigureFig. 7-14Fig. 7-14O E•Circles of isochromesisochromes•Black cross (isogyresisogyres) results from locus of extinction directions•Center of cross (melatopemelatope) represents optic axis•Approx 30o inclination of OA will put it at margin of field of viewUniaxial FigureUniaxial Figure–CenteredCentered axis figure as 7-14: when rotate stage cross does notnot rotate–Off center:Off center: cross still E-W and N-S, but melatopemelatope rotates around center–Melatope outside field:Melatope outside field: bars sweep through, but always N-S or E-W at center–Flash Figure:Flash Figure: OA in plane of stage Diffuse black fills field brief time as rotateFig. 7-14Fig. 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)Biaxial 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


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UVM GEOL 135 - Lecture 9 - Optics II

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