Today’s objectives

1. Today’s objectives • What happens when light passes through most minerals? • 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? • Why do those colors go to black every 90 degrees of rotation? • How can we use those colors to help us identify unknown minerals?

2. Background • Vectors • Light as wave • Interference (2D) • Interference (3D)

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

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

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

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

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

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

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

11. Recap - Pleochroism • Anisotropic grain has fast and slow directions • In 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 displayed

12. D=l/2 1.5  1  slow fast monochromatic! Retardation • fast & slow rays are 45° from polarizer • D = d (ns - nf) • distance, nm d

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

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

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 relationship between the retardation distance, grain thickness, and indices of refraction is: • D = d (ns - nf) • If the new vibration direction is 0° or 180° from the incoming, the ray is canceled at the analyzer (upper polar) • when D=l, or D=2l , or D=3l , or D=4l , etc.

16. slow fast Extinction • When fast or slow direction || polarizer • will occur every 90° of stage rotation • Calcite demo

17. D=l/2 1.5  1  slow fast monochromatic! Interference Colors • What changes for other colors (wavelengths)? • D = d (ns - nf) d

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

19. Thickness effect • D = d (ns - nf) • quartz wedge demo • d = (ns - nf) = 0.009 (a small value) • shows change in set of transmitted wavelengths (i.e., color) with increasing retardation, D

20. Birefringence effect • D = d (ns - nf) = d d • can get same set of colors by varying d at constant d • maximum d is characteristic of mineral! • e.g., calcite d = 0.172 (a large value) • orientation-dependent • d (=ns-nf) ranges from 0 to a maximum • 0 is looking down optic axis

21. Interference Color Chart • range of colors - same as quartz wedge • measuring birefringence birefringence, d quartz? thickness, d (µm) birefringence, d retardation, D (nm)

22. Orders Every 550 nm (≈ lblue) Interference Color Chart birefringence, d thickness, d (µm) birefringence, d retardation, D (nm)

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

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

25. Questions to think about • 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?

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

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

28. Using accessory plates XP • 1) Find vibration directions, using extinction • 2) Rotate so vibration directions are “diagonal” • 3) Insert plate • 4) If colors “add”, slowmineral || slowplate, otherwise, slowmineral || fastplate D=200 nm

29. Using accessory plates XP • 1) Find vibration directions, using extinction • 2) Rotate so vibration directions are “diagonal” • 3) Insert plate • 4) If colors “add”, slowmineral || slowplate, otherwise, slowmineral || fastplate q p

30. Using accessory plates 45° XP • 1) Find vibration directions, using extinction • 2) Rotate so vibration directions are “diagonal” • 3) Insert plate • 4) If colors “add”, slowmineral || slowplate, otherwise, slowmineral || fastplate q p

31. Using accessory plates XP • 1) Find vibration directions, using extinction • 2) Rotate so vibration directions are “diagonal” • 3) Insert plate • 4) If colors “add”, slowmineral || slowplate, otherwise, slowmineral || fastplate q p

32. Using accessory plates XP • 1) Find vibration directions, using extinction • 2) Rotate so vibration directions are “diagonal” • 3) Insert plate • 4) If colors “add”, slowmineral || slowplate, otherwise, slowmineral || fastplate p = slow q p D=750 nm