1. Optical Mineralogy in a Nutshell
Use of the petrographic microscope in three easy lessons
Part II
© Jane Selverstone, University of New Mexico, 2003

2. Quick review
Isotropic minerals –velocity changes as light enters mineral, but then is the same in all directions thru xtl; no rotation or splitting of light.
These minerals are characterized by a single RI (because light travels w/ same speed throughout xtl)
Anisotropic minerals –light entering xtls is split and reoriented into two plane-polarized components that vibrate perpendicular to one another and travel w/ different speeds.
Uniaxial minerals have one special direction along which light is not reoriented; characterized by 2 RIs.
Biaxial minerals have two special directions along which light is not reoriented; characterized by 3 RIs.

3. We’ve talked about minerals as magicians - now let’s prove it!
calcite
calcite
calcite
calcite
calcite
ordinary
ray, w
(stays stationary)
extraordinary
ray, e
(rotates)

4. Conclusions from calcite experiment
single light ray coming into cc is split into two
rays are refracted different amounts
rays have different velocities, hence different RIs
stationary ray=ordinary, rotating ray=extraordinary
because refraction of e is so large, cc must have hi d (remember: d = nhi - nlo)
If we were to look straight down c-axis, we would see only one star – no splitting!
C-axis is optic axis
(true for all uniaxial minerals, but unfortunately not for biaxial minerals)
More on this in a few minutes…

5. Back to birefringence/interference colors
Observation: frequency of light remains unchanged during splitting, regardless of material
mineral grain
plane polarized light
fast ray (low n)
slow ray
(high n)
lower polarizer
D=retardation d
F= V/l if light speed changes, l must also change
l is related to color; if l changes, color also changes

6. Interference phenomena
Light waves may be in phase or out of phase when they exit xtl
When out of phase, some component of light gets through upper polarizer and displays an interference color
When one of the vibration directions is parallel to the lower polarizer, no light gets through the upper polarizer and the grain is “at extinction” (=black)
See Nesse p. 41, 46-48…

7. D = thickness of t.s. x birefringence
At time t, when slow ray 1st exits xtl:
Slow ray has traveled distance d
Fast ray has traveled distance d+D
mineral grain
plane polarized light
fast ray (low n)
slow ray
(high n)
lower polarizer
D=retardation d
time = distance/rate
Slow ray: t = d/Vslow
Fast ray: t= d/Vfast + D/Vair
Therefore: d/Vslow = d/Vfast + D/Vair
D = d(Vair/Vslow - Vair/Vfast)
D = d(nslow - nfast)
D = d d
D = thickness of t.s. x birefringence

8. Birefringence/interference colors
Thickness in microns
Retardation in nanometers

9. Remember determining optic sign last week with the gypsum plate?
slow
blue in NE = (+)
Gypsum plate has constant D of nm = 1st-order pink
Isogyres = black: D=0
Background = gray: D=100
Add or subtract 530 nm:
=630 nm = blue = (+)
=430 nm = yellowish = (-)
Addition = slow + slow
Subtraction = slow + fast

10. Uh oh... Let’s look at interference colors in a natural thin section:
Note that different grains of the same mineral show different interference colors – why?? ol
plag
Uh oh...
If every grain of the same mineral looks different, how are we ever going to be able to identify anything??
Different grains of same mineral are in different orientations

11. 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?

12. 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)

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

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

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

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

17. 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

18. 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

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

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

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

22. … 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

23. 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

24. How interference figures work (uniaxial example)
Converging lenses force light rays to follow different paths through the indicatrix
Bertrand
lens
N-S polarizer
What do we see??
Sample
(looking down OA) nw ne
Effects of multiple cuts thru indicatrix
substage
condensor W E

25. 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°
See Nesse p. 103

26. 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°
See Nesse p. 101
(+)

27. 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.