Transcript Optics II

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)
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?
w
e
polarizer
Michel-Lévy Color Chart – Plate 4.11
Example: Quartz w = 1.544
e = 1.553
Data from Deer et al
Rock Forming Minerals
John Wiley & Sons
What interference color is this?
Colors one observes when polars are crossed (XPL)
Color can be quantified numerically:
d = nhigh - nlow
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
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)
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
Uniaxial indicatrix
c-axis
c-axis
tangerine = uniaxial (-)
Spaghetti squash = uniaxial (+)
quartz
calcite
Uniaxial indicatrix
Circular section is perpendicular to the stem (c-axis)
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
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
anisotropic minerals - biaxial indicatrix
clinopyroxene
feldspar
Now things get a lot more complicated…
anisotropic minerals - uniaxial indicatrix
c-axis
c-axis
calcite
quartz
Let’s perform the same thought experiment…
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?
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
Conoscopic Viewing
A condensing lens below the stage and a
Bertrand lens above it
Arrangement essentially folds planes  cone
Fig 7-13 Bloss, Optical
Crystallography, MSA
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
How interference figures work (uniaxial example)
What do we see??
Bertrand
lens
N-S polarizer
Sample
(looking down OA)
sub-stage
condenser
W
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!!
E-W polarizer
© Jane Selverstone, University of New Mexico, 2003
Uniaxial Interference
Figure
O
E
• Circles of isochromes
Fig. 7-14
• 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
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
Fig. 7-14
– 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
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)
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 -)
… 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
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°
(-)
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
Use this figure to get sign and 2V:
(+)
2V=20°
2V=40°
2V=60°
X
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.
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?
Go to your book…
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•
•
•
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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