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.
• 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.
These minerals are characterized by a single RI
(because light travels w/ same speed throughout xtl)
3. Determining optic sign
Now determine the optic sign of the mineral:
1. Rotate stage until isogyre is concave to NE (if biaxial)
2. Insert gypsum accessory plate
3. Note color in NE, immediately adjacent to isogyre --
Blue = (+)
Yellow = (-)
Uniaxial
Biaxial
(+)
(+)
4. We’ve talked about minerals splitting light -
here’s what it looks like.
calcite calcite
ordinary
ray, w
(stays stationary)
extraordinary
ray, e
(rotates)
5. • single light ray coming into cc is split into two
• e ray is refracted - changes direction & speed
• rays have different velocities, hence different RIs
• stationary ray=ordinary, rotating ray=extraordinary
• because refraction of e is so large, Calcite must have hi d
(remember: d = nhi - nlo)
Conclusions from calcite experiment
If we were to look straight down c-axis, we would see
only one dot – no splitting!
The c-axis is the optic axis for Calcite
(true for all Uniaxial minerals, but unfortunately not for Biaxial minerals)
7. Back to birefringence/interference colors
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 changes
• waves from the two rays can be in
phase or out of phase upon leaving
the crystal
mineral
grain
plane polarized
light
fast ray
(low n)
slow ray
(high n)
lower polarizer
D=retardation
d
8. • When waves are in phase, all light gets killed
• When waves are out of phase, some component of light
gets through upper polarizer and the grain displays an
interference color; color depends on retardation
• When one of the vibration directions is parallel to the
Interference phenomena
lower polarizer, no
light gets through
the upper polarizer and
the grain is “at
extinction” (=black)
9. mineral
grain
plane polarized
light
fast ray
(low n)
slow ray
(high n)
lower polarizer
D=retardation
d
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
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
10. 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
ol
ol
ol
ol
ol plag
plag
plag
plag
plag
plag
Different grains of same mineral are in different orientations
11. Time for another concept: 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
Soccer ball
(or an orange)
Light travels the same
distance in all directions;
n is same everywhere,
thus d = nhi-nlo = 0 = black
13. anisotropic minerals - uniaxial indicatrix
quartz
calcite
c-axis
c-axis
Let’s perform the same thought experiment…
17. nw - nw = 0
therefore, d=0: grain stays bla
(same as the isotropic case)
ne
nw a=X
c=Z
b=Y
nw
n
w
Propagate light along the c-axis,
note what happens to it in plane of
18.
19.
20. Grain changes color upon rotation.
Grain will go black whenever indicatrix
axis is E-W or N-S
ne
n
w
This orientation will show the maximum d of the mineral
n
e
n
w
ne - nw > 0
therefore, d > 0
N
S
W E
Now propagate light perpendicular to c-axis
21. anisotropic minerals - biaxial indicatrix
clinopyroxene
feldspar
Now things get a lot more complicated…
23. Alas, the potato (indicatrix) can have any orientation
within a biaxial mineral…
c
a
b
Z
X
Y
Y
a
Z
b
X
c
olivine augite
(cpx)
24. … 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
25. OA OA
2Vz
Y
X
Z
n
n
n
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 fi
More in a few minutes
26. How interference figures work (Uniaxial example)
Bertrand
lens
Sample
(looking down OA)
substage
condensor
Converging lenses force light
rays to follow different paths
through the indicatrix
W E
N-S polarizer What do we see?
Effects of multiple cuts thru indicatrix
e
w
e
w
e
w
e
w
28. a. Specific gravity of barite is greater than quartz
b. Calcite and dolomite can be distinguished by an acid
test
c. Rhodochrosite is a mineral distinguished by its colour
d. Kyanite and andalusite show double hardness
29. Quick review of why we use indicatrix:
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
OA OA
2Vz
Y
X
Z
n
n
n
hi d
OA OA
2Vz
Y
X
Z
n
n
n
lo d
Isotropic? Uniaxial? Biaxial? Sign? 2V?
All of these help us to uniquely identify unknown minerals.
