2. 1 Today’s objectives What happens when light passes through most minerals?What happens when light passes through most minerals? Why do some minerals change color when the microscope stage is rotated (without analyzer)?Why do some minerals change color when the microscope stage is rotated (without analyzer)? What causes the colors you saw when you inserted the analyzer?What causes the colors you saw when you inserted the analyzer? Why do those colors go to black every 90 degrees of rotation?Why do those colors go to black every 90 degrees of rotation? How can we use those colors to help us identify unknown minerals?How can we use those colors to help us identify unknown minerals?

3. 2 Background VectorsVectors Light as waveLight as wave Interference (2D)Interference (2D) Interference (3D)Interference (3D)

4. 3 Polarization Light can be constrained to vibrate in a particular planeLight can be constrained to vibrate in a particular plane When two light rays combine, their vibration vectors add (vector-wise)When two light rays combine, their vibration vectors add (vector-wise) A B C A+B=CA+B=C

5. 4 Polarization Polaroid film (in the polarizer & analyzer on your scope) absorbs light vibrating perpendicular to it’s directionPolaroid film (in the polarizer & analyzer on your scope) absorbs light vibrating perpendicular to it’s direction incoming ray polarizer direction transmitted component

6. 5 Anisotropic materials Cause light to split into 2 rays vibrating 90° to each otherCause light to split into 2 rays vibrating 90° to each other Two rays “see” a different crystal environmentTwo rays “see” a different crystal environment –different indices of refraction different speeds of lightdifferent speeds of light –different paths produces double refractionproduces double refraction polarized

7. 6 Double refraction Calcite demoCalcite demo –One ray takes unexpected path through crystal (extraordinary,  ´ or E´ ray) –Special direction where this doesn’t happen: optic axis –calcite n  = 1.658 and n  ´ = 1.486 –which image looks “deeper”?

8. 7

9. 8 Pleochroism Two rays are absorbed differentlyTwo rays are absorbed differently –can show different color (distribution of wavelengths) –or intensity of color fast ray slow ray

10. 9 Pleochroism Isometric - no pleo.Isometric - no pleo. Hexagonal, tetragonal - 2 “end- member” colorsHexagonal, tetragonal - 2 “end- member” colors Triclinic, Monoclinic, Orthorhombic - 3 “end-members”Triclinic, Monoclinic, Orthorhombic - 3 “end-members”

11. 10 Pleochroism Isometric - no pleo.Isometric - no pleo. Hexagonal, tetragonal - 2 “end- member” colorsHexagonal, tetragonal - 2 “end- member” colors Triclinic, Monoclinic, Orthorhombic - 3 “end-members”Triclinic, Monoclinic, Orthorhombic - 3 “end-members”

12. 11 Recap - Pleochroism Anisotropic grain has fast and slow directionsAnisotropic grain has fast and slow directions In some minerals, these show different colorsIn some minerals, these show different colors Because the incoming light is polarized, when one ray is perpendicular to that direction, it is excluded and the other color is displayedBecause the incoming light is polarized, when one ray is perpendicular to that direction, it is excluded and the other color is displayed

13. 12 monochromatic! Retardation fast & slow rays are 45° from polarizerfast & slow rays are 45° from polarizer  = d (n s - n f )  = d (n s - n f ) –distance, nm 1 1.5 fast slow  = /2 d

14. 13 Interference Retarded rays get vector-combined in analyzer (“XP”)Retarded rays get vector-combined in analyzer (“XP”) fast slow  = /2 Retardation of /2 causes change in vibration direction of 90° (full transmission)

15. 14 Interference If  =n (n=1,2,3...), no ray passes analyzerIf  =n (n=1,2,3...), no ray passes analyzer Retardation of  causes change in vibration direction of 180° (no transmission) fast slow  =

16. 15 Recap: Retardation / Interference The slow ray is held back, so at the analyzer they combine with a new net vibration direction (retardation changes vibration direction)The slow ray is held back, so at the analyzer they combine with a new net vibration direction (retardation changes vibration direction) The relationship between the retardation distance, grain thickness, and indices of refraction is:The relationship between the retardation distance, grain thickness, and indices of refraction is: –  = d (n s - n f ) If the new vibration direction is 0° or 180° from the incoming, the ray is canceled at the analyzer (upper polar)If the new vibration direction is 0° or 180° from the incoming, the ray is canceled at the analyzer (upper polar) –when  =, or  =2 , or  =3 , or  =4 , etc.

17. 16 When fast or slow direction || polarizerWhen fast or slow direction || polarizer –will occur every 90° of stage rotation Calcite demoCalcite demo fast slowExtinction

18. 17 monochromatic! Interference Colors What changes for other colors (wavelengths)?What changes for other colors (wavelengths)?  = d (n s - n f )  = d (n s - n f ) 1 1.5 fast slow  = /2 d

19. 18 Interference Colors Story above was for one wavelength (color) of lightStory above was for one wavelength (color) of light Retardation distance (  ) is ~same across colors, but:Retardation distance (  ) is ~same across colors, but: –  = n -> no ray (rotation = 0° or 180°) –  = [n - ( /2)] -> max.ray (rot.=90°, 270°) Certain wavelengths get blocked at analyzer, others passCertain wavelengths get blocked at analyzer, others pass –produces an “interference color”

20. 19 Thickness effect  = d (n s - n f )  = d (n s - n f ) quartz wedge demoquartz wedge demo –  = (n s - n f ) = 0.009 (a small value) –shows change in set of transmitted wavelengths (i.e., color) with increasing retardation, 

21. 20 Birefringence effect  = d (n s - n f ) = d   = d (n s - n f ) = d  –can get same set of colors by varying  at constant d maximum  is characteristic of mineral!maximum  is characteristic of mineral! –e.g., calcite  = 0.172 (a large value) orientation-dependentorientation-dependent –  (=n s -n f ) ranges from 0 to a maximum –0 is looking down optic axis

22. 21 Interference Color Chart thickness, d (µm) retardation,  (nm) birefringence,  quartz? range of colors - same as quartz wedgerange of colors - same as quartz wedge measuring birefringencemeasuring birefringence

23. 22 Interference Color Chart thickness, d (µm) retardation,  (nm) birefringence,  OrdersOrders Every 550 nm (≈ blue )Every 550 nm (≈ blue )

24. 23 Interference Color Chart Two kinds of whiteTwo kinds of white –low-order –high-order  = 0.172 d = 30 µm what color is out here?

25. 24 Next Lecture How do you know which “white” you’re looking at?How do you know which “white” you’re looking at? –Wedge effect, gypsum plate Mineral ID features: sign of elongation, extinction type/angleMineral ID features: sign of elongation, extinction type/angle Which is the slow ray,  or  ?Which is the slow ray,  or  ? –Uniaxial indicatrix, conoscopic illumination How are biaxial minerals different?How are biaxial minerals different? –Biaxial indicatrix, conoscopic illumination

26. 25 Questions to think about How many pleochroic colors would a mineral show that stayed black in XP?How many pleochroic colors would a mineral show that stayed black in XP? Before polarizing film, microscopes used a Nicol prism, made of two specially-cut pieces of calcite, glued together. How could you cut calcite to make this work?Before polarizing film, microscopes used a Nicol prism, made of two specially-cut pieces of calcite, glued together. How could you cut calcite to make this work?

27. 26 fast slow 550 nm Accessory plates Tell you fast vs. slow directionsTell you fast vs. slow directions –Fig. 7.21, p. 129 Can add or subtract retardation:Can add or subtract retardation: –Gypsum plate has  = 550 nm (“ ”) –Mica plate has  = 138 nm (“ /4”) Short dimension is always slowShort dimension is always slow 100 nm 450 nm

28. 27 Accessory plates Tell you fast vs. slow directionsTell you fast vs. slow directions –Fig. 7.21, p. 129 Can add or subtract retardation:Can add or subtract retardation: –Gypsum plate has  = 550 nm (“ ”) –Mica plate has  = 138 nm (“ /4”) Short dimension is always slowShort dimension is always slow 100 nm 650 nm fast slow 550 nm

29. 28 Using accessory plates 1) Find vibration directions, using extinction1) Find vibration directions, using extinction 2) Rotate so vibration directions are “diagonal”2) Rotate so vibration directions are “diagonal” 3) Insert plate3) Insert plate 4) If colors “add”, slow mineral || slow plate, otherwise, slow mineral || fast plate4) If colors “add”, slow mineral || slow plate, otherwise, slow mineral || fast plate XP  =200 nm

30. 29 Using accessory plates 1) Find vibration directions, using extinction1) Find vibration directions, using extinction 2) Rotate so vibration directions are “diagonal”2) Rotate so vibration directions are “diagonal” 3) Insert plate3) Insert plate 4) If colors “add”, slow mineral || slow plate, otherwise, slow mineral || fast plate4) If colors “add”, slow mineral || slow plate, otherwise, slow mineral || fast plate p q XP

31. 30 Using accessory plates 1) Find vibration directions, using extinction1) Find vibration directions, using extinction 2) Rotate so vibration directions are “diagonal”2) Rotate so vibration directions are “diagonal” 3) Insert plate3) Insert plate 4) If colors “add”, slow mineral || slow plate, otherwise, slow mineral || fast plate4) If colors “add”, slow mineral || slow plate, otherwise, slow mineral || fast plate p q XP 45°

32. 31 Using accessory plates 1) Find vibration directions, using extinction1) Find vibration directions, using extinction 2) Rotate so vibration directions are “diagonal”2) Rotate so vibration directions are “diagonal” 3) Insert plate3) Insert plate 4) If colors “add”, slow mineral || slow plate, otherwise, slow mineral || fast plate4) If colors “add”, slow mineral || slow plate, otherwise, slow mineral || fast plate p q XP

33. 32 Using accessory plates 1) Find vibration directions, using extinction1) Find vibration directions, using extinction 2) Rotate so vibration directions are “diagonal”2) Rotate so vibration directions are “diagonal” 3) Insert plate3) Insert plate 4) If colors “add”, slow mineral || slow plate, otherwise, slow mineral || fast plate4) If colors “add”, slow mineral || slow plate, otherwise, slow mineral || fast plate p q XP p = slow  =750 nm