1. Light ray overview
Rays are split into 2 orthogonal rays (e and w) – these rays are slowed to different degrees (apparent birefringence, d related to the refractive index, n; d=ne-nw), and can go in different directions, resulting in a different length to get through a mineral (retardation, D, which is a function of both birefringence and thickness of the mineral)

2. When the rays exit the crystal they recombine
Polarized light going into the crystal splits  into two rays, going at different velocities
one is O-ray with n = w
other is E-ray with n = e
When the rays exit the crystal they recombine
When rays of different wavelength
combine  what things happen? e w
polarizer

3. Michel-Lévy Color Chart – Plate 4.11

4. 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

5. What interference color is this?

6. Color can be quantified numerically: d = nhigh - nlow
Colors one observes when polars are crossed (XPL)
Color can be quantified numerically: d = nhigh - nlow

7. Rotation of crystal? Retardation also affected by mineral orientation!
As you rotate a crystal, observed birefringence colors change
Find maximum interference color for each in practice

8. Extinction
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 of elongation based on the use of an accessory plate made of gypsum or quartz (which has a retardation of 550 nm) which changes the color  for a grain at 45º from extinction look for yellow (fast) or blue (slow)

9. Time for some new tricks: the optical indicatrix
Thought experiment:
Consider an isotropic mineral (e.g., garnet)
Imagine point source of light at garnet center; turn light on for fixed amount of time, then map out distance traveled by light in that time
What geometric shape is defined by mapped light rays?

10. Isotropic indicatrix
Light travels the same distance in all directions;
n is same everywhere, thus d = nhi-nlo = 0 = black
Soccer ball
(or an orange)

11. Uniaxial indicatrix calcite quartz c-axis c-axis
tangerine = uniaxial (-)
calcite
Spaghetti squash = uniaxial (+)
quartz

12. Uniaxial indicatrix
Circular section is perpendicular to the stem (c-axis)

13. Propagate light along the c-axis, note what happens to it in plane of thin section
nw - nw = 0
therefore, d=0: grain stays black
(same as the isotropic case) nw

14. This orientation will show the maximum d of the mineral
Now propagate light perpendicular to c-axis N S W E
ne - nw > 0
therefore, d > 0 ne nw ne nw ne nw ne nw ne nw
Grain changes color upon rotation. Grain will go black whenever indicatrix axis is E-W or N-S
This orientation will show the maximum d of the mineral

15. Biaxial indicatrix (triaxial ellipsoid)
The potato!
2Vz
There are 2 different ways to cut this and get a circle…

16. Alas, the potato (indicatrix) can have any orientation within a biaxial mineral…
augite
olivine

17. anisotropic minerals - biaxial indicatrix
feldspar
clinopyroxene
Now things get a lot more complicated…

18. anisotropic minerals - uniaxial indicatrix
c-axis
Let’s perform the same thought experiment…
c-axis
calcite
quartz

19. Uniaxial indicatrix (biaxial ellipsoid)
What can the indicatrix tell us about optical properties of individual grains?

20. 2V: a diagnostic property of biaxial minerals
When 2V is acute about Z: (+)
When 2V is acute about X: (-)
When 2V=90°, sign is indeterminate
When 2V=0°, mineral is uniaxial
2V is measured using an interference figure…
More in a few minutes

21. Conoscopic Viewing
A condensing lens below the stage and a Bertrand lens above it
Arrangement essentially folds planes ® 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

22. How interference figures work (uniaxial example)
What do we see??
Bertrand
lens nw ne
N-S polarizer
Sample
(looking down OA)
Interference figure provides a zoomed ‘picture’ of the optic axes and the areas around that which have rays which are split and refracted – must be gathered in line with optic axis!!
sub-stage
condenser W
E-W polarizer
© Jane Selverstone, University of New Mexico, 2003

23. Uniaxial Interference Figure
O E
Uniaxial Interference Figure
Circles of isochromes
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. Optic Sign Find NE-SW quadrants of the field
Slide the full wave (550nm) plate (aka gypusm plate) in
This slows the ray aligned NE-SW relative to the retardation - if that ray is more retarded it turns blue (adds 550 nm of retardation)

26. Biaxial Minerals – Optic Axes
Biaxial Minerals have 2 optic axes
Recall that biaxial minerals are of lower symmetry crystal classes (orthorhombic, monoclinic, and triclinic)
The plane containing the 2 optic axes is the optic plane  looking down either results in extinction in XPL-no retardation, birefringence
The acute angle between the 2 different optic axes is the 2V angle  how this angle relates to the velocities of refracted rays in the crystal determines the sign (+ or -)

27. … but there are a few generalizations that we can make
The potato has 3 perpendicular principal axes of different length – thus, we need 3 different RIs to describe a biaxial mineral
X direction = na (lowest)
Y direction = nb (intermed; radius of circ. section)
Z direction = ng (highest)
Orthorhombic: axes of indicatrix coincide w/ xtl axes
Monoclinic: Y axis coincides w/ one xtl axis
Triclinic: none of the indicatrix axes coincide w/ xtl axes

28. Biaxial interference figures
There are lots of types of biaxial figures… we’ll concentrate on only two
1. Optic axis figure - pick a grain that stays dark on rotation
Will see one curved isogyre
determine sign w/ gyps
(+)
(-)
determine 2V from curvature of isogyre
90°
60°
40°

29. Biaxial interference figures
2. Bxa figure (acute bisectrix) - obtained when you are looking straight down between the two O.A.s. Hard to find, but look for a grain with intermediate d.
Use this figure to get sign and 2V:
2V=20°
2V=40°
2V=60°
(+)

30. Isotropic? Uniaxial? Biaxial? Sign? 2V?
Quick review:
Indicatrix gives us a way to relate optical phenomena to crystallographic orientation, and to explain differences between grains of the same mineral in thin section
hi d
lo d
Isotropic? Uniaxial? Biaxial? Sign? 2V?
All of these help us to uniquely identify unknown minerals.

31. Review – techniques for identifying unknown minerals
Start in PPL:
Color/pleochroism
Relief
Cleavages
Habit
Then go to XPL:
Birefringence
Twinning
Extinction angle
And Confocal lense:
Uniaxial or biaxial?
2V if biaxial
Positive or negative?

32. Go to your book… Chemical formula Symmetry
Uniaxial or biaxial, (+) or (-)
RIs: lengths of indicatrix axes
Birefringence (d) = N-n
2V if biaxial
Diagrams:
Crystallographic axes
Indicatrix axes
Optic axes
Cleavages
Extinction angles