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Optical Mineralogy
Wave Theory
= 2 X Amplitude
Frequency = # of waves/sec to pass a given
point (hz)
f = v/l
v = velocity
Electromagnetic spectrum & visible portion
Violet (400 nm)  Red (700 nm)
White = ROYGBV
(can be separated by dispersion)
Refraction
Incident ray and reflected ray:
1)  of incidence i =  of reflection r'
2) coplanar “plane of incidence”
Incident
i
air
r’
Reflected
(in plane ^ interface)
Refracted ray:
1) Slower in water (or glass)
2)  r   I
Depends on D v
water
r
Refracted
Index of refraction
For a substance x:
nx = vair/vx
nair = ??
light is slower in water, glass, crystals
Is nwater greater or less than 1??
Larger n associated with slower V !!
Snells Law:
ni sin i = nr sin r
for 2 known media (air/water) sin i/sin r = nr / ni = const
So can predict angle change!
Polarization
Non-polarized (“usual”) light:
Each photon vibrates as a wave form in a single plane
Light beam = numerous photons, each vibrating in a
different plane
Vibration in all directions ~ perpendicular to propagation
direction
Polarization
incoming ray is non-polarized
reflected and refracted rays
both become polarized
Polarization
Microscopes have two polarizers:
polarizer (below stage) is E-W
 analyzer (above stage) is N-S

The Optical Indicatrix
Shows how ni varies with vibration direction.
Vectors radiating from center
Length of each proportional to ni for light vibrating in the
direction of the vector
Indicatrix = surface connecting tips of vectors
(a shape to represent changes in n with direction)
Isotropic media have all ni the same (by definition)
What is the shape of an isotropic indicatrix?
a spherical indicatrix
North
South
A
P
Fig. 6-6
P
A
Fig 6-6 Bloss, Optical
Crystallography, MSA
West
East
P
P
The Optical
Indicatrix
For isotropic minerals
When analyzer inserted
= crossed-nicols or
XPL shorthand (vs
PPL) no light passes
 extinct, even
when the stage is
rotated
Anisotropic crystals
Calcite experiment and double refraction
Anisotropic crystals
Calcite experiment and double refraction
O
Double images:
E
Ray  2 rays with
different propagation
and vibration directions
Each is polarized ( ^ each
other)
Fig 6-7 Bloss, Optical
Crystallography, MSA
Anisotropic crystals
Calcite experiment and double refraction
O
O-ray (Ordinary)
E
Obeys Snell's Law and goes
straight
Vibrates ^ plane containing
ray and c-axis (“optic axis”)
E-ray (Extraordinary)
deflected
Vibrates in plane containing
ray and c-axis
Fig 6-7 Bloss, Optical
Crystallography, MSA
..also doesn't vibrate ^
propagation, but we'll ignore
this as we said earlier
O
IMPORTANT: A given ray of
incoming light is restricted to only 2
(mutually perpendicular) vibration
directions once it enters an
anisotropic crystal
E
Called privileged directions
Each ray has a different n
w = no
e = nE
w < e (in the case of calcite)
Fig 6-7 Bloss, Optical
Crystallography, MSA
n > 1 for all anisotropic substances
n = f(vibration direction)
Indicatrix no longer a sphere
Indicatrix = ellipsoid
Hexagonal and tetragonal xls have one unique xl axis (c
axis) ^ 2 identical ones --UNIAXIAL MINERALS
The optical properties reflect this as well: ellipsoid of
rotation about c
Fig 6-10 Bloss, Optical
Crystallography, MSA
For light
travelling parallel
c, all vibration
directions ^c are
the same:
circular section of indicatrix ( ^ c)
thus behaves as isotropic
(no unique plane containing ray and c-axis)
only one ray (O-ray) with n = w (doesn’t split to two rays)
extinct with analyzer in and stays that way as rotate stage

Fig. 6-12
For light travelling ^ c get
elliptical principal section
of indicatrix:
get 2 rays
O-ray with n = w
E-ray with n = e
this e (parallel c) is the
maximum possible deviation
in n from w (true e)

For random vibration direction  same situation as above
Except that E-ray has some n between e and w
All intermediate values are called e’ (a variable value between
e and w)
ellipsoid and conventions:
(+) crystal = prolate e > w
 (-) crystal = oblate e < w

Fig 6-11 Bloss, Optical
Crystallography, MSA
(-) crystal:
w>e
 oblate
(+) crystal:
e>w
 prolate
Summary:

Circular Section
(^ optic axis: all w's)
 extinct

Fig. 6-12

Principal Sections
(have w and true e: max & min
n's) largest birefringence!


Random Sections (e' and w)

always have w!!
Any cut through center of a
uniaxial indicatrix will have w
as one semiaxis
Color chart
Shows the relationship between retardation, crystal
thickness, and interference color

550 mm
 red violet

800 mm
 green

1100 mm


 red-violet again (note repeat )
0-550 mm = “1st order”
550-1100 mm = 2nd
order 1100-1650 mm = 3rd order...
Higher orders are more pastel
Example: Quartz w = 1.544
e = 1.553
Data from Deer et al
Rock Forming Minerals
John Wiley & Sons
Example: Quartz w = 1.544
e = 1.553
Sign??
(+) because e > w
e - w = 0.009 and is called the birefringence (d)
= maximum interference color


What color is this??
1) Follow line 0.009 in toward origin
2) Where it crosses 30 micron thickness (the standard for thin
sections) we get a yellowish tan (see when quartz oriented with OA
in plane of stage)
For other orientations get e' - w  progressively lower
color

Extinct when priv. direction N-S (every 90o)
360o rotation  4 extinction positions exactly 90o apart
Conoscopic Viewing
A condensing lens below the stage and a Bertrand
lens above it
Arrangement essentially folds planes of Fig 7-11  cone
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
Fig 7-13 Bloss, Optical
Crystallography, MSA
 Interference Figures Very
useful for determining optical
properties of xl
Uniaxial Figure
Fig. 7-14

Circles of isochromes

Note vibration directions:

w tangential

e' radial & variable magnitude

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
Fig 8-1 Bloss, Optical
Crystallography, MSA
Accessory Plates

Use a 1st-order red (gypsum) plate

Slow direction is marked N on plate

Fast direction (n) || axis of plate

The gypsum crystal is oriented and cut so that
D = (N-n)  550nm retardation
 thus it has the effect of retarding the N ray
550 nm behind the n ray

If insert with no crystal on the stage  1order red in whole field of view
Accessory Plates
n
N Suppose we view an anisotropic crystal with
D = 100 nm (1-order gray) at 45o from extinction
If Ngyp || Nxl  Addition
Addition since ray in xl || Ngyp
already behind by 100nm & it gets
further retarded by 550nm in the
gypsum plate
100 + 550  650nm
On your color chart what will result?
o
o
Original 1 grey  2 blue
Optic Sign Determination
For all xls remember e' vibrates in plane of ray
and OA, w vibr normal to plane of ray and
OA
O
w
e'
e'
w
E
e' w
e'
(+) crystals:
e’ > w
so w faster
w
1) Find a uniaxial crystal in which the optic
axis (OA) is vertical (normal to the stage)
How?
2) Go to high power, insert condensing and
Bertrand lenses to  optic axis
interference figure
Fig 7-13 Bloss, Optical
Crystallography, MSA
Optic Sign Determination
Inserting plate for a (+) crystal:
w
e'
sub add
add sub
e'
w
 subtraction in NW & SE where n||N
e' w
 addition in NE & SW where N||N
Whole NE (& SW) quads add 550nm
e' w

(+) crystals:
e’ > w
so w faster
isochromes shift up 1 order
Isogyre adds  red
In NW & SE where subtract

Each isochrome loses an order
Near isogyre (~100nm)

get yellow in NW & SE

and blue in NE & SW
(+) OA Figure without plate
(+) OA Figure with plate
Yellow in NW is (+)
(-) OA Figure without plate
(same as (+) figure)
(-) OA Figure with plate
Blue in NW is (-)
Estimating birefringence
1) Find the crystal of interest showing the
highest colors (D depends on orientation)
2) Go to color chart
thickness = 30 microns (but slides can be thick!)
use 30 micron line + color, follow radial line through
intersection to margin & read birefringence
Suppose you have a mineral with second-order green
What about third order yellow?
Pleochroism
Changes in absorption color in PPL as
rotate stage (common in biotite,
amphibole…)
Pleochroic formula:

Tourmaline:

e = dark green to bluish
w = colorless to tan
Can determine this as just described by
isolating first w and then e E-W and
observing the color

Biaxial Crystals
Orthorhombic, Monoclinic, and Triclinic xls don't have
2 or more identical crystallographic axes


The indicatrix is a general ellipsoid with three unequal,
mutually perpendicular axes
One is the smallest possible n and one the largest
Fig 10-1 Bloss, Optical
Crystallography, MSA
a = smallest n
b = intermediate n
g = largest n
(fastest)
(slowest)
The principal vibration directions
are x, y, and z ( x || a, y || b, z || g)
By definition a < a' < b < g '< g
g
Biaxial Crystals
If a < b < g then there must be some point
between a & g with n = b
Because =b in plane, and true b is normal to
plane, then the section containing both is a
circular section
=b
Has all of the properties of a circular section! If
a look down it:
all rays = b
no preferred vibration direction
polarized incoming light will remain so
thus appear isotropic as rotate stage
Looking down true b
g
Biaxial Crystals
If a < b < g then there must be some point
between a & g with n = b
OA
^ optic axis by definition
=b
a
Looking down true b
Biaxial Crystals
g
OA
If a < b < g then there must be some point
between a & g with n = b
OA
^ optic axis by definition
And there must be two!  Biaxial
=b
Hexagonal and tetragonal are Uniaxial
a
=b
Looking down true b
Biaxial Crystals
Nomenclature:


Fig 10-2 Bloss, Optical
Crystallography, MSA
2 circular sections
 2 optic axes
Must be in a-g
plane = Optic
Axial Plane (OAP)
Y || b direction ^
OAP = optic
normal
•Acute angle between OA's = 2V
•The axis that bisects acute angle = acute bisectrix = Bxa
•The axis that bisects obtuse angle = obtuse bisectrix = Bxo
Biaxial Crystals
g
OA
B(+) defined as Z (g) = Bxa
Thus b closer to a than to g
OA
=b
a
=b
Looking down true b
Biaxial Crystals
g
B(-) defined as X (a) = Bxa
Thus b closer to g than to a
=b
OA
a
OA
=b
Looking down true b
Biaxial Interference Figures
Fig 10-15 Bloss, Optical
Crystallography, MSA
Bxa figure
Result is this pattern
of isochromes for
biaxial crystals
Biaxial Interference Figures
Centered Bxa Figure
Fig 10-16 Bloss, Optical
Crystallography, MSA
Biaxial Interference Figures
Same figure rotated 45o
Optic axes are now E-W
Clearly isogyres must swing
Fig 10-16B Bloss, Optical
Crystallography, MSA
As rotate
Centered Optic Axis Figure Large 2V:
Not much
curvature
Bxa Figure with Small 2V:
Biaxial Optic Sign
B(-)
a = Bxa thus b closer to g
100 gray + 550
 650 blue
add
subtract
add
Fig. 11-1A
100 gray - 550
 450 yellow
Biaxial Optic Sign
B(-) a = Bxa thus b closer to g (in stage)
add
Centered Bxa 2V = 35o
Centered Bxa 2V = 35o
With accessory plate
subtract
add
Biaxial Optic Sign
B(+) g = Bxa thus b closer to a (in stage)
sub
add
sub
Fig. 11-1A
Estimating 2V
OAP
Fig 11-5A Bloss, Optical
Crystallography, MSA