1. Isotropic vs Anisotropic
Many optical methods to distinguish isotropic and anisotropic minerals
Distinction of two types important
Know if isometric system or not
If anisotropic, we’ll see there are ways to identify individual systems.
Primary method is observations of extinction

2. Polarizing Microscope
Ocular
Analyzer, upper polarizer, nicols lens
Objective
Polarizer, typically oriented N-S

3. Not Extinct
Extinct
Quartz crystals in plane polarized light
Same quartz crystals with analyzer inserted (cross polarizers aka crossed nicols)

4. Feldspar partially extinct,
One grain
Individual crystals
Feldspar partially extinct,

5. Extinction in muscovite
Extinction in calcite

6. Isotropic Minerals Easily identified
Always extinct with upper polarizer inserted
That is no light passes the upper analyzer
Rotate stage and remains extinct
Vibration direction not changed by material
All light blocked by upper polarizer

7. Polarizing Microscope
Ocular
Analyzer, upper polarizer, nicols lens
Objective
Polarizer, typically oriented N-S

8. Anisotropic Minerals Variable values of n within mineral
Has property of double refraction
Light entering material usually split into two rays
Two rays vibrate perpendicular to each other
Caveat: Special section of minerals: light not split and behaves like isotropic mineral – called optic axis
All other orientations: light splits into two rays

9. Optic axis Special direction where rays not split into two rays
Wave normal and ray path coincide
Hexagonal and tetragonal have one optic axis
Uniaxial
Orthorhombic, monoclinic, and triclinic have two optic axes
Biaxial

10. So… light usually split into two rays
For each of the two light rays:
Value of n is determined by vibration direction
In one direction, the value of n is larger than the other
Direction with large N is slow ray
Direction with small n is fast ray
Different values of n mean different angles of refraction – “double refraction”

11. Interference Phenomena
For most cuts of anisotropic minerals, light not completely blocked by analyzer
Specific color is interference color
Caused by two rays resolving to one ray when they leave the mineral

12. Interference Colors “Intermediate” interference colors
Not true colors
Viewed in crossed nicols (upper polarizer inserted)
“Intermediate” interference colors
“Low interference colors”

13. Colored minerals Biotite, a pleochroic mineral, natural color
Cross nicols
Viewed in plane polarized light
Biotite, a pleochroic mineral, natural color
Muscovite showing interference colors

14. YouTube video of pleochroism and interference colors
Glaucophane – an amphibole: Na2Mg3Al2Si8O22 (OH) 2

15. Interference with monochromatic light
Monochromatic = one wavelength
Light split into fast and slow ray
Fast ray travels farther than slow ray in same time
Difference in the distances called retardation, D
Retardation remains same after two rays leave mineral (air is isotropic)

16. f = v/l; f constant so l changes
Note: here you need to imagine the two rays follow the same path even though they are refracted
D = extra distance fast ray traveled
Distance for slow ray
Distance for fast ray
d = thickness (distance)
Typically 30 µm
f = v/l; f constant so l changes
Fig. 7-14

17. Retardation and Birefringence
Derive definition of retardation

18. Retardation controlled by two things:
Thickness of mineral, d
Difference in speed of fast and slow ray –
(ns – nf) – must be positive number
Units have to be length, typically reported as nm

19. Birefringence Birefringence is the difference between ns and nf
d = (ns – nf)

20. f = v/l; f constant so l changes
Note: here you need to imagine the two rays follow the same path even though they are refracted
D = extra distance fast ray traveled
Distance for slow ray
Distance for fast ray
d = thickness (distance)
Typically 30 µm
f = v/l; f constant so l changes
Fig. 7-14

21. Origin of interference colors
Still talking about monochromatic light
If retardation is an integer number of wavelengths:
Components resolve into vibration direction same as original direction
All light is blocked by analyzer

22. Original polarized direction
D = 1,2,3… l
Privileged direction of analyzer
Resolved vibration direction – Identical to original direction
All light blocked = extinct
Resolved vibration direction
Fig. 7-15a

23. If retardation is half integer of wavelength
Components resolve into vibration direction 90º to original
Light passes through analyzer

24. Fig. 7-15b Original polarized direction
Resolved vibration directions
90º to original direction
Privileged direction of analyzer
D = ½, 3/2, 5/2… l
All light passes
Fig. 7-15b

25. Fig. 7-4 bloss A more realistic depiction
Note – this is still monochromatic light
1½ l 1l 2l 2l
From Bloss, 1961

26. Interference with polychromatic light
All wavelengths
Some l = integer value of D
Most l ≠ integer value of D
Interference colors depend on what wavelengths are allowed to pass through analyzer
The wavelengths depend on retardation (D = d*d)

27. Depending on magnitude of birefringence:
If a narrow band of wavelengths passes through analyzer, see only one color
Sometimes multiple l pass through analyzer, see white

28. For standard thin section (d=30µm) Interference colors are:
Visible l
All pass through
Quartz: D = 250 nm
1st order white
Kyanite: D = 500 nm;
1st order red
Violet
Red
500/500 = 1
Blue is blocked
750/500 = 1.5 (half integer)
750 l passes through
Calcite: D = 2500 nm;
4th order white; cream
2500/416.6 = 6
2500/500 = 5
2500/625= 4
Green
Red
Indigo
416.6, 500, 625 l = full integer, blocked – combined to make white
Fig. 7-17

29. Interference Colors “2nd – 3rd order reds and blues” “1st order gray”
Not true colors
Viewed in crossed nicols (upper polarizer inserted)
“2nd – 3rd order reds and blues”
“1st order gray”

30. Color chart Shows range of interference colors
depends on retardation
Plot of d (thickness of thin section) versus D (retardation)
Diagonal lines are birefringence, d = ns - nf

31. Color chart Divided into orders Orders are in multiples of 550 nm
Successively higher orders are increasingly washed out
Above 4th order, color becomes creamy white
Retardation D (nm)

32. Color chart Two Primary uses:
Determine birefringence of mineral
Determine thickness of thin sections
Recall retardation controlled by thickness and birefringence; D = dd
Retardation is simply the observed interference color, D
E.g., the sum of wavelengths that are half integers of retardation.

33. Determining thickness of thin section
Use quartz (or other easily identifiable, common mineral)
Maximum d is 0.009
From back of book: ns = 1.553; nf = 1.544
Actual birefringence depends on orientation of grain
Page 232

34. Maximum birefringence & retardation when c axis is parallel to stage
Birefringence & retardation = 0 when c axis is perpendicular to stage (optic axis)
Intermediate birefringence & retardation for intermediate orientation

35. Procedure
Find quartz with highest birefringence (correct cut of mineral)
Done by scanning many quartz crystals
Find where the retardation (given by color), intersects lines for birefringence
Calculate it from formula for birefringence: d=D/d
Or read off thickness from chart

36. Fig.7-18

37. Typical slide thickness is 30 µm (0.03 mm)
Quartz will be first order white to yellow
Thin sections may not be perfect
Variable thicknesses
Thin on edges
Thick sections – 70 µm
Used for inclusions
Freeze/thaw of fluid inclusions

38. Determining birefringence
Maximum d is a useful diagnostic value
Gives the nmaximum and nmiminum of grain
Easily determined in thin section with known thickness
Distribution of birefringence:
Some with zero d
Some with maximum d
Most with intermediate d

39. Procedure for determining birefringence
Find grain with highest interference colors – most likely to have fastest and slowest n values
Find retardation on the basis of the color (bottom of chart)
Calculate the birefringence using equation: d=D/d
Or find maximum birefringence from chart

40. Fig. 7-18b

41. Extinction
Many grains in a thin section go dark (extinct) every 90º of rotation
Cause for extinction is orientation of vibration directions
Occurs when principle vibration directions are parallel to vibration directions of upper and lower polarizers
Light retains original polarized direction
Light blocked by analyzer

42. Extinction Ocular Analyzer, upper polarizer, nicols lens
Polarizer, typically oriented N-S

43. Extinct
Birefringent
Fig 7-19

44. Importance of extinction
Allows determination of principle vibration directions
When extinct, the orientation of the principle vibration directions are N-S and E-W

45. Extinction in muscovite
Extinction in calcite

46. Accessory Plates Primary functions: Determine optic sign
Determine sign of elongation

47. Microscopy Ocular Analyzer, upper polarizer, nicols lens
Accessory Slot
Polarizer, typically oriented N-S

48. Construction: Usually gypsum - full wave plate, D = 550 nm
Common mica - ½ wave plate, D = 150 nm
Retardation is known
Orientation of principle vibration directions is known, set at 45º to polarizer and analyzer
Fast ray is length of holder, slow ray is perpendicular to holder

49. Interference of accessory plate either adds or subtracts from retardation of mineral
With slow ray of mineral parallel slow ray of accessory plate – retardation increases
With slow ray of mineral parallel fast ray of accessory plate – retardation decreases

50. Net result:
Accessory plate tells you orientation of fast and slow direction in mineral
Important for many optical observations

51. Total – greater than before – slow on slow - addition
D mineral
Total – greater than before – slow on slow - addition
D Total – less than before – slow on fast - subtraction
D mineral
D total
Fig. 7-20

52. Procedure to determine fast and slow
Rotate grain to extinction – either fast or slow ray parallel to polarized light direction
Rotate stage 45º
Note interference color
Insert accessory plate
Observe if color increases or decreases (right or left on chart)

53. Interference plate will also determine order of interference color
(1) extinction
(3) Insert accessory plate
If colors increase after insertion – slow on slow
(2) Rotate 45º
Fig. 7-21