1. Frequency = # of waves/sec to pass a given point (hz)
Optical Mineralogy
Wave Theory
= 2 X Amplitude
Frequency = # of waves/sec to pass a given point (hz)
f = v/l v = velocity

2. Electromagnetic spectrum & visible portion
Violet (400 nm)  Red (700 nm)
White = ROYGBV
(can be separated by dispersion)

3. Refraction Incident ray and reflected ray: Refracted ray:
1)  of incidence i =  of reflection r'
2) coplanar “plane of incidence”
(in plane ^ interface)
Refracted ray:
1) Slower in water (or glass)
2)  r   I
Depends on D v
Incident i
Reflected r’
air
water r
Refracted

4. Index of refraction For a substance x: nx = vair/vx nair =
Index of refraction For a substance x: nx = vair/vx nair = ?? light is slower in water, glass, crystals Is nwater greater or less than 1?? Larger n associated with slower V !! Snells Law: ni sin i = nr sin r for 2 known media (air/water) sin i/sin r = nr / ni = const So can predict angle change!

5. Polarization Non-polarized (“usual”) light:
Each photon vibrates as a wave form in a single plane
Light beam = numerous photons, each vibrating in a different plane
Vibration in all directions ~ perpendicular to propagation direction

6. Polarization incoming ray is non-polarized
reflected and refracted rays
both become polarized

7. Polarization Microscopes have two polarizers:
polarizer (below stage) is E-W
analyzer (above stage) is N-S

8. The Optical Indicatrix
Shows how ni varies with vibration direction.
Vectors radiating from center
Length of each proportional to ni for light vibrating in the direction of the vector
Indicatrix = surface connecting tips of vectors
(a shape to represent changes in n with direction)
Isotropic media have all ni the same (by definition)
What is the shape of an isotropic indicatrix?
a spherical indicatrix

9. The Optical Indicatrix
North
South A P P
For isotropic minerals
When analyzer inserted = crossed-nicols or XPL shorthand (vs PPL) no light passes
 extinct, even when the stage is rotated
Fig. 6-6 A
Fig 6-6 Bloss, Optical Crystallography, MSA
West P P
East

10. Anisotropic crystals
Calcite experiment and double refraction

11. Anisotropic crystals Calcite experiment and double refraction
O E
Double images:
Ray  2 rays with different propagation and vibration directions
Each is polarized ( ^ each other)
Fig 6-7 Bloss, Optical Crystallography, MSA

12. Anisotropic crystals Calcite experiment and double refraction
O E
O-ray (Ordinary)
Obeys Snell's Law and goes straight
Vibrates ^ plane containing ray and c-axis (“optic axis”)
E-ray (Extraordinary)
deflected
Vibrates in plane containing ray and c-axis
..also doesn't vibrate ^ propagation, but we'll ignore this as we said earlier
Fig 6-7 Bloss, Optical Crystallography, MSA

13. Called privileged directions Each ray has a different n w = no e = nE
IMPORTANT: A given ray of incoming light is restricted to only 2 (mutually perpendicular) vibration directions once it enters an anisotropic crystal
Called privileged directions
Each ray has a different n
w = no
e = nE
w < e (in the case of calcite)
O E
Fig 6-7 Bloss, Optical Crystallography, MSA

14. n > 1 for all anisotropic substances
n = f(vibration direction)
Indicatrix no longer a sphere
Indicatrix = ellipsoid
Hexagonal and tetragonal xls have one unique xl axis (c axis) ^ 2 identical ones --UNIAXIAL MINERALS
The optical properties reflect this as well: ellipsoid of rotation about c

15. Fig 6-10 Bloss, Optical Crystallography, MSA
For light travelling parallel c, all vibration directions ^c are the same:
circular section of indicatrix ( ^ c)
thus behaves as isotropic
(no unique plane containing ray and c-axis)
only one ray (O-ray) with n = w (doesn’t split to two rays)
extinct with analyzer in and stays that way as rotate stage

16. For light travelling ^ c get elliptical principal section of indicatrix:
get 2 rays
O-ray with n = w
E-ray with n = e
this e (parallel c) is the maximum possible deviation in n from w (true e)
Fig. 6-12
For random vibration direction  same situation as above
Except that E-ray has some n between e and w
All intermediate values are called e’ (a variable value between e and w)

17. ellipsoid and conventions:
(+) crystal = prolate e > w
(-) crystal = oblate e < w
(-) crystal:
w > e
 oblate
(+) crystal:
e > w
 prolate
Fig 6-11 Bloss, Optical Crystallography, MSA

18. Summary: Circular Section Principal Sections
(^ optic axis: all w's)
extinct
Principal Sections
(have w and true e: max & min n's) largest birefringence!
Random Sections (e' and w)
always have w!!
Any cut through center of a uniaxial indicatrix will have w as one semiaxis
Fig. 6-12

19. Color chart
Shows the relationship between retardation, crystal thickness, and interference color
550 mm ® red violet
800 mm ® green
1100 mm ® red-violet again (note repeat )
0-550 mm = “1st order” mm = 2nd order mm = 3rd order...
Higher orders are more pastel

20. Example: Quartz w = 1.544 e = 1.553 w e 1.544 1.553
Data from Deer et al
Rock Forming Minerals John Wiley & Sons

21. Example: Quartz w = 1.544 e = 1.553 Sign?? (+) because e > w
e - w = and is called the birefringence (d) = maximum interference color
What color is this??
1) Follow line in toward origin
2) Where it crosses 30 micron thickness (the standard for thin sections) we get a yellowish tan (see when quartz oriented with OA in plane of stage)
For other orientations get e' - w ® progressively lower color
Extinct when priv. direction N-S (every 90o)
360o rotation ® 4 extinction positions exactly 90o apart

22. Conoscopic Viewing
A condensing lens below the stage and a Bertrand lens above it
Arrangement essentially folds planes of Fig ® cone
Light rays are refracted by condensing lens & pass through crystal in different directions
Thus different properties
Only light in the center of field of view is vertical & like ortho
® Interference Figures Very useful for determining optical properties of xl
Fig 7-13 Bloss, Optical Crystallography, MSA

23. Uniaxial Figure Circles of isochromes Note vibration directions:
w tangential
e' radial & variable magnitude
Black cross (isogyres) results from locus of extinction directions
Center of cross (melatope) represents optic axis
Approx 30o inclination of OA will put it at margin of field of view
Fig. 7-14

24. Uniaxial Figure
Centered axis figure as 7-14: when rotate stage cross does not rotate
Off center: cross still E-W and N-S, but melatope rotates around center
Melatope outside field: bars sweep through, but always N-S or E-W at center
Flash Figure: OA in plane of stage Diffuse black fills field brief time as rotate
Fig. 7-14

25. Accessory Plates Use a 1st-order red (gypsum) plate
Fig 8-1 Bloss, Optical Crystallography, MSA
Use a 1st-order red (gypsum) plate
Slow direction is marked N on plate
Fast direction (n) || axis of plate
The gypsum crystal is oriented and cut so that D = (N-n) ® 550nm retardation
 thus it has the effect of retarding the N ray 550 nm behind the n ray
If insert with no crystal on the stage ® 1- order red in whole field of view

26. Accessory Plates N
Suppose we view an anisotropic crystal with D = 100 nm (1-order gray) at 45o from extinction n
If Ngyp || Nxl ® Addition
Addition since ray in xl || Ngyp
already behind by 100nm & it gets further retarded by 550nm in the gypsum plate
® 650nm
On your color chart what will result?
Original 1o grey ® 2o blue N

27. Optic Sign Determination
For all xls remember e' vibrates in plane of ray and OA, w vibr normal to plane of ray and OA
O E e ' w
1) Find a uniaxial crystal in which the optic axis (OA) is vertical (normal to the stage) How?
2) Go to high power, insert condensing and Bertrand lenses to ® optic axis interference figure
(+) crystals:
e’ > w
so w faster

28. Fig 7-13 Bloss, Optical Crystallography, MSA

29. Optic Sign Determination
Inserting plate for a (+) crystal:
® subtraction in NW & SE where n||N
® addition in NE & SW where N||N
Whole NE (& SW) quads add 550nm
isochromes shift up 1 order
Isogyre adds ® red
In NW & SE where subtract
Each isochrome loses an order
Near isogyre (~100nm)
get yellow in NW & SE
and blue in NE & SW e ' w
sub
add
add
sub
(+) crystals:
e’ > w
so w faster N

30. (+) OA Figure with plate
(+) OA Figure without plate
(+) OA Figure with plate
Yellow in NW is (+)

31. (-) OA Figure without plate (same as (+) figure)
(-) OA Figure with plate
Blue in NW is (-)

32. Estimating birefringence
1) Find the crystal of interest showing the highest colors (D depends on orientation)
2) Go to color chart
thickness = 30 microns (but slides can be thick!)
use 30 micron line + color, follow radial line through intersection to margin & read birefringence
Suppose you have a mineral with second-order green
What about third order yellow?

33. Pleochroism
Changes in absorption color in PPL as rotate stage (common in biotite, amphibole…)
Pleochroic formula:
Tourmaline: e = dark green to bluish w = colorless to tan
Can determine this as just described by isolating first w and then e E-W and observing the color

34. Biaxial Crystals
Orthorhombic, Monoclinic, and Triclinic xls don't have 2 or more identical crystallographic axes
The indicatrix is a general ellipsoid with three unequal, mutually perpendicular axes
One is the smallest possible n and one the largest
Fig 10-1 Bloss, Optical Crystallography, MSA
a = smallest n (fastest)
b = intermediate n
g = largest n (slowest)
The principal vibration directions are x, y, and z ( x || a, y || b, z || g)
By definition a < a' < b < g '< g

35. Biaxial Crystals g
If a < b < g then there must be some point between a & g with n = b
Because =b in plane, and true b is normal to plane, then the section containing both is a circular section
Has all of the properties of a circular section! If look down it:
all rays = b
no preferred vibration direction
polarized incoming light will remain so
thus appear isotropic as rotate stage
= b a
Looking down true b

36. Biaxial Crystals ^ optic axis by definition g
If a < b < g then there must be some point between a & g with n = b OA
^ optic axis by definition
= b a
Looking down true b

37. Biaxial Crystals ^ optic axis by definitiong
If a < b < g then there must be some point between a & g with n = b OA OA
^ optic axis by definition
And there must be two!  Biaxial
Hexagonal and tetragonal are Uniaxial
= b a
= b
Looking down true b

38. Biaxial Crystals Nomenclature:
2 circular sections ® 2 optic axes Must be in a-g plane = Optic Axial Plane (OAP)
Y || b direction ^ OAP = optic normal
Fig 10-2 Bloss, Optical Crystallography, MSA
Acute angle between OA's = 2V
The axis that bisects acute angle = acute bisectrix = Bxa
The axis that bisects obtuse angle = obtuse bisectrix = Bxo

39. Biaxial Crystals B(+) defined as Z (g) = Bxa
Thus b closer to a than to g OA OA
= b a
= b
Looking down true b

40. Biaxial Crystals B(-) defined as X (a) = Bxag
B(-) defined as X (a) = Bxa
Thus b closer to g than to a
= b OA a OA
= b
Looking down true b

41. Biaxial Interference Figures
Fig Bloss, Optical Crystallography, MSA
Bxa figure
Result is this pattern of isochromes for biaxial crystals

42. Biaxial Interference Figures
Centered Bxa Figure
Fig Bloss, Optical Crystallography, MSA

43. Biaxial Interference Figures
Same figure rotated 45o
Optic axes are now E-W
Clearly isogyres must swing
Fig 10-16B Bloss, Optical Crystallography, MSA

44. Centered Optic Axis Figure Large 2V:
As rotate
Centered Optic Axis Figure Large 2V:
Bxa Figure with Small 2V:
Not much curvature

45. Biaxial Optic Sign B(-) a = Bxa thus b closer to g add subtract add
100 gray ® 650 blue
Fig. 11-1A
add
subtract
add
100 gray ® 450 yellow

46. Biaxial Optic Sign B(-) a = Bxa thus b closer to g (in stage) add
subtract
Centered Bxa 2V = 35o
Centered Bxa 2V = 35o
With accessory plate

47. Biaxial Optic Sign B(+) g = Bxa thus b closer to a (in stage) sub add
Fig. 11-1A
sub
add
sub

48. Estimating 2V
Fig 11-5A Bloss, Optical Crystallography, MSA
OAP