1. Interference Figures 1. Uniaxial Figures
Optical Mineralogy
Interference Figures
1. Uniaxial Figures

2. Optical Indicatrix and Interference Figures:
LAB TS-3:
Uniaxial minerals
Interference figures
Optic sign
Pleochroic scheme
LAB TS-4:
Biaxial minerals

3. Optical Indicatrix and Interference Figures:
Uniaxial Interference Figures
Biaxial Interference Figures

4. Polarisation in the petrographic microscope
upper polarising filter (analyser)
what happens
here???
LAB TS-2
sensitive tint plate
what happens
here???
LAB TS-1
mineral sample (thin section)
conoscopic light
what happens here???
LAB TS-3,4
condenser lens
plane polarised light (PPL)
lower polarising filter (polariser)
unpolarised light
light source

5. Optical Indicatrix nmax (slow) in 2D: nmin = nmax nmin (fast)
constructed as a sphere or ellipsoid with radii parallel to the principal
vibration directions and lengths of axes proportional to refractive index
nmax
(slow)
in 2D:
nmin = nmax
circle:
isotropic
nmin
(fast)
nmin < nmax
nmin
ellipse:
anisotropic
nmax
in 3D:
indicatrix for isotropic mineral is a sphere (of no further interest)
indicatrix for anisotropic mineral is an ellipsoid
2 cases: uniaxial and biaxial

6. ne < nw -ve ne > nw +ve
Case 1: Uniaxial minerals (hexagonal, tetragonal: a1 = a2 = c)
principal axes: ne // c nw // a
e: “extraordinary” ray w: “ordinary” ray
X = Y < Z
X < Y = Z
Nesse, 2000; Fig. 7.23
Y-Z plane: circular section
(all planes perpendicular to X)
X = optic axis (c-axis = fast)
ne < nw -ve
X-Y plane: circular section
(all planes perpendicular to Z)
Z = optic axis (c-axis = slow)
ne > nw +ve

7. Case 1: Uniaxial minerals (hexagonal, tetragonal: a1 = a2 = c)
principal axes: ne // c nw // a
e: “extraordinary” ray w: “ordinary” ray
optic axis // plane of section
plane of section contains
both nw and ne :
maximum d
random section:
contains nw and
ne’ < ne
intermediate d
optic axis I plane of section
plane of section contains
only nw :
minimum d (extinct!)
Nesse, 2000; Fig. 7.25

8. Optic Sign how do we figure this out??? Case 1: Uniaxial minerals:
Z = optic axis (c-axis = slow)
ne > nw +ve
X = optic axis (c-axis = fast)
ne < nw -ve
Case 2: Biaxial minerals:
+ ve where Bxa // Z
-ve where Bxa // X Z Z
c = OA = Z
+ve
-ve
+ve
c = OA = X
-ve X X a a

9. Optic Sign how do we figure this out??? Requires:
conoscopic light (condenser lens in place)
interference figures (viewed with Bertrand lens)
use of STP to determine fast and slow directions
Nesse, Ch. 7, p (uniaxial)
p (biaxial)
Extinction Angles:
where optic axis is normal to plane of thin section
mineral will appear extinct for full stage rotation!
applies to both uniaxial and biaxial minerals
how distinguished from isotropic minerals?
(also requires interference figures: stay tuned.....)

10. Optical Indicatrix and Symmetry
isometric system: a1 = a2 = a3; all angles = 90o
indicatrix is a sphere; minerals extinct in XN
hexagonal, trigonal, tetragonal systems: a1 = a2 (= a3) = c
all angles either 90o or 120o
uniaxial: indicatrix is ellipsoid; X < Y < Z
c-axis = optic axis = e (either X or Z)
parallel extinction
orthorhombic system: a = b = c; all angles = 90o
biaxial: indicatrix is ellipsoid; X < Y < Z
X, Y, Z // crystallographic axes
2 circular sections I 2 optic axes

11. e can be either fast or slow
2. Uniaxial Interference Figures
(Nesse Ch. 7 p )
optic axis = c crystallographic axis
ne // c; nw // a
e can be either fast or slow

12. Interference Figures result: interference figure
require conoscopic light
Bertrand lens
(on eyepiece tube)
rays focused through
centre of sample:
concentric interference rings
when viewed through Bertrand lens
condenser lens
(sub-stage)
Nesse Fig. 7.36

13. (in XN, grain appears extinct
Interference Figures
result:
interference
figure
uniaxial optic axis figure
isochrome OA
melatope
isogyre OA
number of rings
(isochromes)
 birefringence
sample oriented
with optic axis normal
to plane of section
(in XN, grain appears extinct
through 360o rotation)
Nesse Fig. 7.36

14. Interference Figures what it really looks like:
uniaxial optic axis figure
isochrome
melatope
isochromes
melatope
isogyre
isogyre
number of rings
(isochromes)
 birefringence
cross-hairs
sample oriented
with optic axis normal
to plane of section
(in Xn, grain appears extinct
through 360o rotation)
optic axis figure (OAF)
for high d mineral
(e.g., calcite)

15. (in XN, grain appears extinct
Interference Figures
uniaxial optic axis figure
isochrome
melatope
isogyre w e
number of rings
(isochromes)
 birefringence
Nesse Fig. 7.35
sample oriented
with optic axis normal
to plane of section
(in XN, grain appears extinct
through 360o rotation)
e oriented radially
w oriented tangentially

16. ? ? Interference Figures: w e insert tint plate!
Determining Optic Sign
uniaxial optic axis figure
observe colour
change in
SE-NW
quadrants w ? e ?
if e slow: mineral is +ve
if e fast: mineral is -ve
Nesse Fig. 7.40

17. Interference Figures:
colours
go down
(subtraction)
w = fast
e = slow
Interference Figures:
Determining Optic Sign
down
uniaxial optic axis figure
down
+ ve
colours
go up
(addition)
w = slow
e = fast w up e up
if e slow: mineral is +ve
if e fast: mineral is -ve
- ve

18. Interference Colour Chart
low d optic axis figure
addition:
grey  blue
30 mm
subtraction:
grey  yellow
what do addition and subtraction look like?

19. Interference Colour Chart
low d optic axis figure
high d optic axis figure
addition:
2nd order red  3rd order red
addition:
grey  blue
30 mm
subtraction:
grey  yellow
subtraction:
2nd order red  1st order red
what do addition and subtraction look like?

20. Interference Figures:
colours
go down
(subtraction)
w = fast
e = slow
Interference Figures:
Determining Optic Sign
uniaxial optic axis figure Y
+ ve
colours
go up
(addition)
w = slow
e = fast Y
SE-NW quadrant:
if colours go from grey-white to yellow
(subtraction; “down”)
mineral is +ve (YAY!)
- ve

21. Interference Figures:
colours
go down
(subtraction)
w = fast
e = slow
Interference Figures:
Determining Optic Sign
uniaxial optic axis figure B
+ ve
colours
go up
(addition)
w = slow
e = fast B
SE-NW quadrant:
if colours go from grey-white to blue
(addition; “up”)
mineral is -ve (BOO!)
- ve

22. Interference Figures:
colours
go down
(subtraction)
w = fast
e = slow
Interference Figures:
Determining Optic Sign
high d mineral (many isochromes) no
tint
plate
+ ve
colours
go up
(addition)
w = slow
e = fast
low order colours (grey-white)
near centre of figure
- ve

23. Interference Figures:
colours
go down
(subtraction)
w = fast
e = slow
Interference Figures:
Determining Optic Sign
high d mineral (many isochromes) no
tint
plate
+ ve
colours
go up
(addition)
w = slow
e = fast
tint plate in +
(rings
move in) -
(rings
move out)
- ve

24. Interference Figures:
colours
go down
(subtraction)
w = fast
e = slow
Interference Figures:
Determining Optic Sign
high d mineral (many isochromes) no
tint
plate
+ ve
colours
go up
(addition)
w = slow
e = fast
tint plate in +
(rings
move in) -
(rings
move out)
- ve
mineral is
uniaxial -ve

25. Interference Figures Practical problem(s):
1. How to find a grain with optic axis normal to plane of
thin section?
2. What if you can’t find a suitably oriented grain?

26. Interference Figures Practical problem(s):
1. How to find a grain with optic axis normal to plane of
thin section?
2. What if you can’t find a suitably oriented grain?
look for grain that is extinct for full rotation of stage (opaque? isotropic? hole in slide? optic axis grain?)

27. Interference Figures Practical problem(s):
1. How to find a grain with optic axis normal to plane of
thin section?
2. What if you can’t find a suitably oriented grain?
look for grain that is extinct for full rotation of stage (opaque? isotropic? hole in slide? optic axis grain?)
look for low d grain with minimum change during rotation “off-centre” figure:
not ideal, but may be best possible in your section

28. Interference Figures OK to use “off-centre” uniaxial figure:
slightly
off-centre
(melatope
visible)
OK to use
Interference Figures
“off-centre” uniaxial figure:
obtained from low d grain with
minimum colour change
during rotation
not ideal, but may be best
possible in your section
way
off-centre
(melatope
not visible)
best
avoided
Nesse Fig. 7.38

29. Interference Figures Flash Figures: both e and w in plane of section
(maximum d)
useless for
determining
optic sign
very similar for both
uniaxial and biaxial
field of view
light  dark
very quickly
as stage
rotated
Nesse Fig. 7.39

30. Uniaxial Minerals: Pleochroic Scheme
Nesse, 2000; Fig. 7.30
In PPL, find grain with minimum colour change as stage rotated
(w in plane of section); observed colour = w (= a)
In PPL, find grain with maximum colour change as stage rotated
(both w and e in plane of section); w colour already determined
other colour = e (= c)
3. Can also be determined by finding fast and slow rays + optic sign

31. Optic Sign: Summary Case 1: Uniaxial minerals:
Z = optic axis (c-axis = slow)
ne > nw +ve
X = optic axis (c-axis = fast)
ne < nw -ve
Case 2: Biaxial minerals:
+ ve where Bxa // Z
-ve where Bxa // X Z Z
c = OA = Z
+ve
-ve
+ve
c = OA = X
-ve X
Bxa X a a
Bxa
determined from OA figure
determined from Bxa or OA figure