Slide 1Slide 2Slide 3Slide 4Slide 5Anisotropic crystalsSlide 7Slide 8‘Splitting’ of light  what does it mean?Difference between our 2 raysSlide 11Slide 12Michel-Lévy Color Chart – Plate 4.11Slide 14Slide 15Slide 16Slide 17Rotation of crystal?ExtinctionSlide 20Twinning and Extinction AngleVernier scaleSlide 23Slide 24Slide 25Slide 26Appearance of crystals in microscopeSlide 28Slide 29light vibrates inall planes that containthe light ray(i.e., all planesperpendicular tothe propagationdirectionplane of vibrationvibration directionpropagation directionWhat happens as light moves through the scope?3) Now insert a thin section of a rockwest (left)east (right)Light vibrating E-WHow does this work??Unpolarized lightLight vibrating in many planes and with many wavelengthsLight and colors reach eye!Some generalizations and vocabulary•All isometric minerals (e.g., garnet) are isotropic – they cannot reorient light. Light does not get rotated or split; propagates with same velocity in all directions–These minerals are always black in crossed polars.•All other minerals are anisotropic – they are all capable of reorienting light (transmit light under cross polars).•All anisotropic minerals contain one or two special directions that do not reorient light.–Minerals with one special direction are called uniaxial–Minerals with two special directions are called biaxial•Isotropic minerals: light does not get rotated or split; propagates with same velocity in all directions•Anisotropic minerals:•Uniaxial - light entering in all but one special direction is resolved into 2 plane polarized components that vibrate perpendicular to one another and travel with different speeds•Biaxial - light entering in all but two special directions is resolved into 2 plane polarized components…–Along the special directions (“optic axes”), the mineral thinks that it is isotropic - i.e., no splitting occurs–Uniaxial and biaxial minerals can be further subdivided into optically positive and optically negative, depending on orientation of fast and slow rays relative to xtl axesIsotropicUniaxialBiaxialHow light behaves depends on crystal structureIsometric– All crystallographic axes are equalOrthorhombic, monoclinic, triclinic–All axes are unequalHexagonal, tetragonal– All axes  c are equal but c is uniqueO EDouble images:Ray  2 rays with different propagation and vibration directionsEach is polarized (  each other)Fig 6-7 Bloss, Optical Crystallography, MSAAnisotropic crystalsAnisotropic crystalsCalcite experiment Calcite experiment and double refractiondouble refractionO-rayO-ray (Ordinary)  ωObeys Snell's Law and goes straightVibrates  plane containing ray and c-axis (“optic axis”)E-rayE-ray (Extraordinary)  εdeflectedVibrates inin plane containing ray and c-axis..also doesn't vibrate  propagation, but we'll ignore thisBoth rays vibrate parallel to the incident surface for normal incident light, so the interface x-section of the indicatrix is still valid, even for the E-rayThus our simplification of vibration  propagation works well enoughFrom now on we'll treat these two rays as collinear, but not interacting, because it's the vibration direction that countsO EFig 6-7 Bloss, Optical Crystallography, MSAIMPORTANT: A given ray of incoming IMPORTANT: A given ray of incoming light is restricted to only 2 (mutually light is restricted to only 2 (mutually perpendicular) vibration directions perpendicular) vibration directions once it enters an anisotropic crystalonce it enters an anisotropic crystalCalled privileged directionsprivileged directionsEach ray has a different n = no = nE in the case of calcite  <  …which makes the O-ray dot appear above E-ray dotIf each ray has a different velocity, then each has a different wavelength because velocity=•If I slow down 1 ray and then recombine it with another ray that is still going faster, what happens??‘Splitting’ of light  what does it mean?•For some exceptionally clear minerals where we can see this is hand sample this is double refraction  calcite displays this•Light is split into 2 rays, one traveling at a different speed, and this difference is a function of thickness and orientation of the crystal  Norden Bombsight patented in 1941 utilized calcite in the lenses to gauge bomb delivery based on speed, altitude of plane vs target•ALL anisotropic minerals have this property, and we can ‘see’ that in thin sections with polarized light!Difference between our 2 rays•Apparent birefringence –  – difference in refractive index (speed) between the 2 rays•Retardation –   distance separating the 2 rays•Retardation therefore is a function of the apparent birefringence and the thickness of the crystal  ideally all thin sections are 0.3 mm, but mistakes do happen…Polarized light going into the crystal splits  into two rays, going at different velocities and therefore at different wavelengths (colors)one 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 4.111) Find the crystal of interest showing the highest colors ( depends on orientation)2) Go to color chartthickness = 30 micronsuse 30 micron line + color, follow radial line through intersection to margin & read birefringenceSuppose you have a mineral with second-order greenWhat about third order yellow?Estimating birefringenceEstimating birefringenceExample: Quartz  = 1.544  = 1.5531.5531.544Data from Deer et al Rock Forming MineralsJohn Wiley & SonsExample: Quartz  = 1.544  = 1.553Sign?? (+) because  >   -  = 0.009 called the birefringencebirefringence () = maximummaximum interference color (when seen?)What color is this?? Use your chart.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