Selverstone optical min 2

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Optical Mineralogy in a Nutshell Use of the petrographic microscope in three easy lessons Part II © 2003 Prof Jane Selverstone Used and modified with permission Quick review • Isotropic minerals –velocity changes as light enters mineral, but then is the same in all directions thru xtl; no rotation or splitting of light These minerals are characterized by a single RI (because light travels w/ same speed throughout xtl) • Anisotropic minerals –light entering xtls is split and reoriented into two plane-polarized components that vibrate perpendicular to one another and travel w/ different speeds • Uniaxial minerals have one special direction along which light is not reoriented; characterized by RIs • Biaxial minerals have two special directions along which light is not reoriented; characterized by RIs Determining if mineral is uniaxial or biaxial or Uniaxial If Uniaxial, isogyres define a cross; arms remain N-S/E-W as stage is rotated Biaxial If Biaxial, isogyres define a curve that rotates with stage, or cross that breaks up as stage is rotated Reminder about how to get an interference figure Find a grain that stays dark as stage is rotated Go to highest power objective Swing the condenser in and open the diaphragm iris Insert the Bertrand Lens (if present) or remove the eyepiece Look down the scope and then rotate stage Determining optic sign Now determine the optic sign of the mineral: Rotate stage until isogyre is concave to NE (if biaxial) Insert gypsum accessory plate Note color in NE, immediately adjacent to isogyre - Blue = (+)  Yellow = (-) Uniaxial Biaxial (+) (-) We’ve talked about minerals splitting light here’s what it looks like calcite ca te lci c al calcite cite calcite ordinary ray, ω (stays stationary) extraordinary ray, ε (rotates) Conclusions from calcite experiment • single light ray coming into cc is split into two • ε ray is refracted - changes direction & speed • rays have different velocities, hence different RIs • stationary ray=ordinary, rotating ray=extraordinary • because refraction of ε is so large, Calcite must have hi δ (remember: δ = nhi - nlo) If we were to look straight down c-axis, we would see only one dot – no splitting! The c-axis is the optic axis for Calcite (true for all Uniaxial minerals, but unfortunately not for Biaxial minerals) Birefringence/interference colors Thickness in microns birefringence Retardation in nanometers Back to birefringence/interference colors ∆=retardation fast ray (low n) slow ray (high n) d mineral grain plane polarized light lower polarizer Observation: frequency of light remains unchanged during splitting, regardless of material F= V/λ if light speed changes, λ must also change ∀λ is related to color; if λ changes, color changes • waves from the two rays can be in phase or out of phase upon leaving the crystal Interference phenomena • When waves are in phase, all light gets killed • When waves are out of phase, some component of light gets through upper polarizer and the grain displays an interference color; color depends on retardation • When one of the vibration directions is parallel to the lower polarizer, no light gets through the upper polarizer and the grain is “at extinction” (=black) At time t, when slow ray 1st exits xtl: Slow ray has traveled distance d Fast ray has traveled distance d+∆ ∆=retardation fast ray (low n) slow ray (high n) d time = distance/rate Slow ray: t = d/Vslow Fast ray: t= d/Vfast + ∆/Vair Therefore: d/Vslow = d/Vfast + ∆/Vair mineral grain ∆ = d(Vair/Vslow - Vair/Vfast) plane polarized light lower polarizer ∆ = d(nslow - nfast) ∆=dδ ∆ = thickness of t.s x birefringence anisotropic minerals - uniaxial indicatrix c-axis c-axis calcite quartz Let’s perform the same thought experiment… Uniaxial indicatrix c-axis Spaghetti squash = Uniaxial (+) quartz c-axis tangerine = Uniaxial (-) calcite The shapes reflect the relative sizes of indices of refraction Uniaxial indicatrix nω nε nω nω Circular section is perpendicular to the stem (c-axis) Uniaxial Indicatrix c=Z c=Z nε nω b=Y nε a=X b=Y nω a=X Uniaxial (-) Uniaxial (+) What can the indicatrix tell us about optical properties of individual grains? Propagate light along the c-axis, note what happens to it in plane of thin section c=Z nε nω b=Y a=X nω nω nω - nω = therefore, δ=0: grain stays black (same as the isotropic case) Now propagate light perpendicular to c-axis N nε - nω > therefore, δ > ω nnε ε n ωnω W nnω nω n nε nε ε E S Grain changes color upon rotation Grain will go black whenever indicatrix axis is E-W or N-S This orientation will show the maximum δ of the mineral anisotropic minerals - biaxial indicatrix clinopyroxene feldspar Now things get a lot more complicated… Biaxial indicatrix (triaxial ellipsoid) OA Z 2Vz OA 2Vz nγ Y nβ nβ nα nβ The potato! X nγ nγ nα nβ nα nβ There are different ways to cut this and get a circle… Alas, the potato (indicatrix) can have any orientation within a biaxial mineral… Y c a Z Z olivine c augite (cpx) b Y b X a X … but there are a few generalizations that we can make The potato has perpendicular principal axes of different length – thus, we need different RIs to describe a biaxial mineral X direction = nα (lowest) Y direction = nβ (intermed; radius of circ section) Z direction = nγ (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 axes 2V: a diagnostic property of biaxial minerals OA Z OA • When 2V is acute about Z: (+) 2Vz • When 2V is acute about X: (-) • When 2V=90°, sign is indeterminate nγ • When 2V=0°, mineral is uniaxial Y nβ nα X 2V is measured using an interference figure… More in a few minutes How interference figures work (Uniaxial example) Converging lenses force light rays to follow different paths through the indicatrix Bertrand lens N-S polarizer What we see? Sample (looking down OA) ω ω substage condensor ε ε ε ω ω ε Effects of multiple cuts thru indicatrix W E Biaxial interference figures There are lots of types of biaxial figures… we’ll concentrate on only two Optic axis figure - pick a grain that stays dark on rotation Will see one curved isogyre determine sign w/ gypsum plate (+) determine 2V from curvature of isogyre 90° 60° 40° See Nesse or handout (-) Biaxial interference figures 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 Z intermediate δ OA OA 2Vz nγ Y nβ nα X Use this figure to get sign and 2V: (+) 2V=20° 2V=40° 2V=60° See handout/Nesse Quick review of why we use indicatrix: Indicatrix gives us a way to relate optical phenomena to crystallographic orientation, and to explain differences between grains of the same mineral in thin section OA Z OA hi δ 2Vz nγ nα nβ Y OA Z X OA lo δ 2Vz nγ Y nβ nα X Isotropic? Uniaxial? Biaxial? Sign? 2V? All of these help us to uniquely identify unknown minerals [...]... curved isogyre determine sign w/ gypsum plate (+) determine 2V from curvature of isogyre 90° 60° 40° See Nesse or handout (-) 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 Z intermediate δ OA OA 2Vz nγ Y nβ nα X Use this figure to get sign and 2V: (+) 2V =20 ° 2V=40° 2V=60° See handout/Nesse... describe a biaxial mineral X direction = nα (lowest) Y direction = nβ (intermed; radius of circ section) Z direction = nγ (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 axes 2V: a diagnostic property of biaxial minerals OA Z OA • When 2V is acute about Z: (+) 2Vz • When 2V is acute about... axes 2V: a diagnostic property of biaxial minerals OA Z OA • When 2V is acute about Z: (+) 2Vz • When 2V is acute about X: (-) • When 2V=90°, sign is indeterminate nγ • When 2V=0°, mineral is uniaxial Y nβ nα X 2V is measured using an interference figure… More in a few minutes How interference figures work (Uniaxial example) Converging lenses force light rays to follow different paths through the indicatrix... will show the maximum δ of the mineral anisotropic minerals - biaxial indicatrix clinopyroxene feldspar Now things get a lot more complicated… Biaxial indicatrix (triaxial ellipsoid) OA Z 2Vz OA 2Vz nγ Y nβ nβ nα nβ The potato! X nγ nγ nα nβ nα nβ There are 2 different ways to cut this and get a circle… Alas, the potato (indicatrix) can have any orientation within a biaxial mineral… Y c a Z Z olivine c... of why we use indicatrix: Indicatrix gives us a way to relate optical phenomena to crystallographic orientation, and to explain differences between grains of the same mineral in thin section OA Z OA hi δ 2Vz nγ nα nβ Y OA Z X OA lo δ 2Vz nγ Y nβ nα X Isotropic? Uniaxial? Biaxial? Sign? 2V? All of these help us to uniquely identify unknown minerals ... thin section: plag ol ol plag ol plag plag plag ol ol ol plag Note that different grains of the same mineral show different interference colors – why? Different grains of same mineral are in different orientations Time for another concept: 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... Uniaxial indicatrix nω nε nω nω Circular section is perpendicular to the stem (c-axis) Uniaxial Indicatrix c=Z c=Z nε nω b=Y nε a=X b=Y nω a=X Uniaxial (-) Uniaxial (+) What can the indicatrix tell us about optical properties of individual grains? Propagate light along the c-axis, note what happens to it in plane of thin section c=Z nε nω b=Y a=X nω nω nω - nω = 0 therefore, δ=0: grain stays black (same as...Determining optic sign with the gypsum plate - what happens? blue in NE = (+) Gypsum plate has constant ∆ of 530 nm = 1st-order pink slo w Isogyres = black: ∆=0 Background = gray: ∆=150 Add to/subtract from... shape is defined by mapped light rays? Isotropic indicatrix Soccer ball (or an orange) Light travels the same distance in all directions; n is same everywhere, thus δ = nhi-nlo = 0 = black anisotropic minerals - uniaxial indicatrix c-axis c-axis calcite quartz Let’s perform the same thought experiment… Uniaxial indicatrix c-axis Spaghetti squash = Uniaxial (+) quartz c-axis tangerine = Uniaxial (-)
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