Optical Mineralogy in a Nutshell
Use of the petrographic microscope in
three easy lessons
Part II
© Jane Selverstone, University of New Mexico, 2003
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.
We’ve talked about minerals as magicians now let’s prove it!
calcite
calcite
ordinary
ray, w
(stays stationary)
extraordinary
ray, e
(rotates)
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…
Back to birefringence/interference colors
D=retardation
fast ray
(low n)
slow ray
(high n)
d
mineral
grain
plane polarized
light
lower polarizer
Observation:
frequency of
light remains unchanged
during splitting,
regardless of material
F= V/l
if light speed changes,
l must also change
l is related to color; if l
changes, color also changes
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…
At time t, when slow ray 1st exits xtl:
Slow ray has traveled distance d
Fast ray has traveled distance d+D
time = distance/rate
D=retardation
fast ray
(low n)
slow ray
(high n)
d
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)
mineral
grain
plane polarized
light
D = d(nslow - nfast)
D=dd
D = thickness of t.s. x birefringence
lower polarizer
Birefringence/interference colors
Thickness in microns
birefringence
Retardation in nanometers
Remember determining optic sign last week with the gypsum plate?
blue in NE = (+)
Gypsum plate has constant D of
530 nm = 1st-order pink
Isogyres = black: D=0
Background = gray: D=100
Add or subtract 530 nm:
530+100=630 nm = blue = (+)
530-100=430 nm = yellowish = (-)
Addition = slow + slow
Subtraction = slow + fast
Let’s look at interference colors in a natural thin section:
plag
ol
Ifoleveryplag
grain
plag
ol
plag
of the same mineral
looks different, how are we
ever going
ol
plag
ol anything??
to be able to identify
ol
plag
Note that different grains of the same mineral show
different interference colors – why??
Different grains of same mineral are in different orientations
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?
Isotropic indicatrix
Soccer ball
(or an orange)
Light travels the same
distance in all directions;
n is same everywhere,
thus d = nhi-nlo = 0 = black
anisotropic minerals - uniaxial indicatrix
c-axis
c-axis
calcite
quartz
Let’s perform the same thought experiment…
Uniaxial indicatrix
c-axis
c-axis
tangerine = uniaxial (-)
Spaghetti squash = uniaxial (+)
quartz
calcite
Uniaxial indicatrix
Circular section is perpendicular to the stem (c-axis)
Uniaxial indicatrix
(biaxial ellipsoid)
c=Z
c=Z
ne
nw
b=Y
ne
a=X
b=Y
nw
a=X
What can the indicatrix tell us about
optical properties of individual grains?
Propagate light along the c-axis, note what
happens to it in plane of thin section
nw
c=Z
n
ne
nw
w
a=X
b=Y
nw - nw = 0
therefore, d=0: grain stays black
(same as the isotropic case)
Now propagate light perpendicular to c-axis
ne - nw > 0
N
therefore, d > 0
n
w
ne
n
w
W
E
ne
S
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
anisotropic minerals - biaxial indicatrix
clinopyroxene
feldspar
Now things get a lot more complicated…
Biaxial indicatrix
2Vz
(triaxial ellipsoid)
Z
OA
OA
2Vz
n
n
n
Y
n
n
The potato!
X
n
n
n
n
n
n
There are 2 different ways to cut this and get a circle…
Alas, the potato (indicatrix) can have any orientation
within a biaxial mineral…
Y c
a
Z
c
olivine
Z
augite
b
Y
b
X
a
X
… 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 = n (lowest)
Y direction = n (intermed; radius of circ. section)
Z direction = n (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
2V: a diagnostic property of biaxial minerals
Z
OA
OA
• When 2V is acute about Z: (+)
2Vz
• When 2V is acute about X: (-)
• When 2V=90°, sign is indeterminate
n
• When 2V=0°, mineral is uniaxial
n
Y
n
X
2V is measured using an interference figure…
More in a few minutes
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)
substage
condensor
Effects of multiple cuts thru indicatrix
W
E
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
(-)
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
Z
intermediate d.
OA
OA
2Vz
n
n
Y
n
X
Use this figure to get sign and 2V:
(+)
2V=20°
2V=40°
2V=60°
See Nesse p. 101
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
Z
OA
OA
hi d
2Vz
n
n
X
n
Y
Z
OA
OA
lo d
2Vz
n
n
Y
n
X
Isotropic? Uniaxial? Biaxial? Sign? 2V?
All of these help us to uniquely identify unknown minerals.