Isotropic vs Anisotropic
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Many optical methods to distinguish
isotropic and anisotropic minerals
Distinction of two types important
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Know if isometric system or not
If anisotropic, we’ll see there are ways to
identify individual systems.
Primary method is observations of
extinction
Polarizing Microscope
Ocular
Analyzer, upper
polarizer, nicols lens
Objective
Polarizer,
typically oriented
N-S
Not
Extinct
Quartz crystals in plane
polarized light
Extinct
Same quartz crystals
with analyzer inserted
(cross polarizers aka
crossed nicols)
One grain
Individual
crystals
Feldspar
partially extinct,
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Extinction in muscovite
Extinction in calcite
Isotropic Minerals
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Easily identified
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Always extinct with upper polarizer inserted
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That is no light passes the upper analyzer
Rotate stage and remains extinct
Vibration direction not changed by material
All light blocked by upper polarizer
Polarizing Microscope
Ocular
Analyzer, upper
polarizer, nicols lens
Objective
Polarizer,
typically oriented
N-S
Anisotropic Minerals
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Variable values of n within mineral
Has property of double refraction
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Light entering material usually split into two
rays
Two rays vibrate perpendicular to each other
Caveat: Special section of minerals: light not
split and behaves like isotropic mineral –
called optic axis
All other orientations: light splits into two rays
Optic axis
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Special direction where rays not split into
two rays
Wave normal and ray path coincide
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Hexagonal and tetragonal have one optic axis
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Uniaxial
Orthorhombic, monoclinic, and triclinic have
two optic axes
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Biaxial
So… light usually split
into two rays
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For each of the two light rays:
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Value of n is determined by vibration direction
In one direction, the value of n is larger than
the other
Direction with large N is slow ray
Direction with small n is fast ray
Different values of n mean different angles of
refraction – “double refraction”
Interference Phenomena
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For most cuts of anisotropic minerals, light
not completely blocked by analyzer
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Specific color is interference color
Caused by two rays resolving to one ray when
they leave the mineral
Interference Colors
Not true colors
Viewed in crossed nicols (upper polarizer inserted)
“Intermediate”
interference colors
“Low interference
colors”
Colored minerals
Viewed in plane polarized light
Biotite, a
pleochroic mineral,
natural color
Cross nicols
Muscovite showing
interference colors
YouTube video of pleochroism
and interference colors
Glaucophane – an amphibole: Na2Mg3Al2Si8O22 (OH) 2
Interference with monochromatic
light
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Monochromatic = one wavelength
Light split into fast and slow ray
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Fast ray travels farther than slow ray in same
time
Difference in the distances called retardation, D
Retardation remains same after two rays leave
mineral (air is isotropic)
Note: here you need to
imagine the two rays follow
the same path even though
they are refracted
D = extra distance
fast ray traveled
Distance for
slow ray
d = thickness
(distance)
Typically 30 µm
Distance for
fast ray
f = v/l; f
constant so l
changes
Fig. 7-14
Retardation and Birefringence
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Derive definition of retardation
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Retardation controlled by two things:
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Thickness of mineral, d
Difference in speed of fast and slow ray –
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(ns – nf) – must be positive number
Units have to be length, typically reported as
nm
Birefringence
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Birefringence is the difference between ns
and nf
d = (ns – nf)
Note: here you need to
imagine the two rays follow
the same path even though
they are refracted
D = extra distance
fast ray traveled
Distance for
slow ray
d = thickness
(distance)
Typically 30 µm
Distance for
fast ray
f = v/l; f
constant so l
changes
Fig. 7-14
Origin of interference colors
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Still talking about monochromatic light
If retardation is an integer number of
wavelengths:
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Components resolve into vibration direction
same as original direction
All light is blocked by analyzer
Original polarized direction
Resolved vibration
direction –
Identical to
original direction
D = 1,2,3… l
Privileged
direction of
analyzer
All light blocked
= extinct
Resolved vibration direction Fig. 7-15a
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If retardation is half integer of wavelength
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Components resolve into vibration direction
90º to original
Light passes through analyzer
Original polarized direction
Resolved
vibration
directions
90º to original
direction
Privileged direction
of analyzer
D = ½, 3/2, 5/2… l
All light passes
Fig. 7-15b
Fig. 7-4 bloss
1½ l
1l
2l
2l
A more
realistic
depiction
Note – this is
still
monochromatic
light
From Bloss, 1961
Interference with polychromatic
light
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Polychromatic light
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All wavelengths
Some l = integer value of D
Most l ≠ integer value of D
Interference colors depend on what
wavelengths are allowed to pass through
analyzer
The wavelengths depend on retardation
(D = d*d)
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Depending on magnitude of birefringence:
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If a narrow band of wavelengths passes
through analyzer, see only one color
Sometimes multiple l pass through analyzer,
see white
For standard thin section
(d=30µm)
Interference colors are:
Red
Quartz: D = 250 nm
1st order white
Kyanite: D = 500 nm;
1st order red
Calcite: D = 2500 nm;
4th order white; cream
Red
2500/625= 4
750/500 = 1.5 (half integer)
750 l passes through
Green
2500/500 = 5
500/500 = 1
Blue is blocked
Indigo
2500/416.6 = 6
Violet
Visible l
All pass through
416.6, 500, 625 l = full
integer, blocked – combined
to make white
Fig. 7-17
Interference Colors
Not true colors
Viewed in crossed nicols (upper polarizer inserted)
“2nd – 3rd order
reds and blues”
“1st order gray”
Color chart
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Shows range of interference colors
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depends on retardation
Plot of d (thickness of thin section) versus D
(retardation)
Diagonal lines are birefringence, d = ns - nf
Color chart
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Divided into orders
Orders are in multiples of 550 nm
Successively higher orders are increasingly washed out
Above 4th order, color becomes creamy white
Retardation D (nm)
Color chart
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Two Primary uses:
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Determine birefringence of mineral
Determine thickness of thin sections
Recall retardation controlled by thickness
and birefringence; D = dd
Retardation is simply the observed
interference color, D
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E.g., the sum of wavelengths that are half
integers of retardation.
Determining thickness of thin
section
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Use quartz (or other easily
identifiable, common
mineral)
Maximum d is 0.009
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From back of book: ns =
1.553; nf = 1.544
Actual birefringence depends
on orientation of grain
Page 232
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Maximum birefringence & retardation
when c axis is parallel to stage
Birefringence & retardation = 0 when c
axis is perpendicular to stage (optic axis)
Intermediate birefringence & retardation
for intermediate orientation
Procedure
Find quartz with highest birefringence
(correct cut of mineral)
1.
1.
2.
3.
4.
Done by scanning many quartz crystals
Find where the retardation (given by
color), intersects lines for birefringence
Calculate it from formula for
birefringence: d=D/d
Or read off thickness from chart
Fig.7-18
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Typical slide thickness is 30 µm (0.03 mm)
Quartz will be first order white to yellow
Thin sections may not be perfect
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Variable thicknesses
Thin on edges
Thick sections – 70 µm
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Used for inclusions
Freeze/thaw of fluid inclusions
Determining birefringence
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Maximum d is a useful diagnostic value
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Gives the nmaximum and nmiminum of grain
Easily determined in thin section with
known thickness
Distribution of birefringence:
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Some with zero d
Some with maximum d
Most with intermediate d
Procedure for determining
birefringence
1.
2.
3.
4.
Find grain with highest interference
colors – most likely to have fastest and
slowest n values
Find retardation on the basis of the color
(bottom of chart)
Calculate the birefringence using
equation: d=D/d
Or find maximum birefringence from
chart
Fig. 7-18b
Extinction
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Many grains in a thin section go dark
(extinct) every 90º of rotation
Cause for extinction is orientation of
vibration directions
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Occurs when principle vibration directions are
parallel to vibration directions of upper and
lower polarizers
Light retains original polarized direction
Light blocked by analyzer
Extinction
Ocular
Analyzer, upper
polarizer, nicols lens
Polarizer,
typically oriented
N-S
Extinct
Birefringent
Fig 7-19
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Importance of extinction
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Allows determination of principle vibration
directions
When extinct, the orientation of the principle
vibration directions are N-S and E-W
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Extinction in muscovite
Extinction in calcite
Accessory Plates
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Primary functions:
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Determine optic sign
Determine sign of elongation
Microscopy
Ocular
Analyzer, upper
polarizer, nicols lens
Accessory Slot
Polarizer,
typically oriented
N-S
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Construction:
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Usually gypsum - full wave plate, D = 550 nm
Common mica - ½ wave plate, D = 150 nm
Retardation is known
Orientation of principle vibration directions is
known, set at 45º to polarizer and analyzer
Fast ray is length of holder, slow ray is
perpendicular to holder
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Interference of accessory plate either adds
or subtracts from retardation of mineral
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With slow ray of mineral parallel slow ray of
accessory plate – retardation increases
With slow ray of mineral parallel fast ray of
accessory plate – retardation decreases
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Net result:
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Accessory plate tells you orientation of fast
and slow direction in mineral
Important for many optical observations
D mineral
D Total – greater
than before –
slow on slow addition
D Total – less
than before –
slow on fast subtraction
D mineral
D total
Fig. 7-20
Procedure to determine fast and
slow
1.
2.
3.
4.
5.
Rotate grain to extinction – either fast or
slow ray parallel to polarized light
direction
Rotate stage 45º
Note interference color
Insert accessory plate
Observe if color increases or decreases
(right or left on chart)
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Interference plate will also determine
order of interference color
(1) extinction
(3) Insert
accessory plate
If colors increase after insertion –
slow on slow
(2) Rotate 45º
Fig. 7-21