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Optical Mineralogy
WS 2008/2009
Next week ….
So far ….
• Light - properties and behaviour;
• Refraction - the refractive index (n) of minerals leads to
many of their optical properties  Snell’s law - learn it!;
• Double refraction;
• Polarization and the polarizing microscope;
• Plane polarised light observations (PPL):
• crystal shape/habit
• colour/pleochroism
• cleavage/fracture
• relief, Becke test  refractive index estimation
Crystal systems and symmetry
The crystal systems are sub-divided by their degree of symmetry….
CUBIC > TETRAGONAL, HEXAGONAL, TRIGONAL >
ORTHORHOMBIC, MONOCLINIC, TRICLINIC
The Optical Indicatrix
• The optical indicatrix is a 3-dimensional graphical
representation of the changing refractive index of a
mineral;
• The shape of the indicatrix reflects the crystal system
to which the mineral belongs;
• The distance from the centre to a point on the surface
of the indicatrix is a direct measure of n at that point.
The Optical Indicatrix
The simplest case - cubic minerals (e.g. garnet)
• Cubic minerals have highest
symmetry (a=a=a);
• If this symmetry is reflected in the
changing refractive index of the
mineral, what 3-d shape will the
indicatrix be?
Isotropic indicatrix (= cubic)
Sphere
n is constant is every direction isotropic minerals do not change the
vibration direction of the light - no
polarisation
Indicatrix = 3-d representation of refractive index
Isotropic indicatrix
Isotropic minerals and polarized light
West (links)
z.B. Granat
Norden
(hinten)
Süden
(vorne)
Ost (rechts)
Polarisator
Schwarz!!
Analysator
Beobachtungen unter gekreuzten Polarisatoren
(gekreuzte Nicols)
XPL = crossed nicols (crossed polars)
Anisotropic minerals – Double refraction
Example: Calcite




The incident ray is split into 2 rays that
vibrate perpendicular to each other.
These rays have variable v (and therefore
variable n)  fast and slow rays
One of the rays (the fast ray for calcite)
obeys Snell’s Law - ordinary ray (no)
The other ray does not obey Snell’s law extraordinary ray (ne)
 Birefringence = Δn = ne − no
Anisotropic Minerals – The Uniaxial Indicatrix
c-axis
Quartz
c-axis
Calcite
What does the indicatrix for each mineral look like?
Uniaxial indicatrix – ellipsoid of rotation
c=Z
optic axis ≡ c-axis
c=X
ne
no
ne
no
b=Y=X
a=X
a=X
NOTE:
no = n 
nen
ne > no
ne < no
uniaxial positive (+)
uniaxial negative (-)
PROLATE or ‘RUGBY BALL‘
OBLATE or ‘SMARTIE‘
b=Y
Quartz
Calcite
ne > no
ne < no
uniaxial positive
uniaxial negative
Uniaxial Indicatrix
All minerals belonging to the TRIGONAL, TETRAGONAL
and HEXAGONAL crystal systems have a uniaxial
indicatrix….
This reflects the dominance of the axis of symmetry (= c-axis)
in each system (3-, 4- and 6-fold respectively)….
Different slices through the indicatrix (+)

Basal section
Cut perpendicular to the optic axis: only no
 No birefringence (isotropic section)

Principal section
Parallel to the optic axis: no & ne
 Maximum birefringence

Random section
 ne' and no
 ne' is between ne and no
 Intermediate birefringence

All sections contain no!
Basal Section
Cut PERPENDICULAR to the caxis,
Contains only no (n)
c=Z
n
n
a=X
b=Y
Isotropic section
(remains black in XN)
Principal Section
Cut PARALLEL to the c-axis,
contains no (n) und ne (n)
n > n 
The principal section shows MAXIMUM
birefringence and the HIGHEST polarisation colour
 DIAGNOSTIC PROPERTY OF
MINERAL
Random Section
Cut at an angle to the c-axis,
contains no (n) und ne‘ (n‘)
A random section shows an intermediate
polarisation colour
 no use for identification purposes
Double Refraction
Privileged Vibration directions
In any random cut through an anistropic
indicatrix, the privileged vibration directions are
the long and short axis of the ellipse. We know
where these are from the extinction positions….
Parallel position
Polariser parallel to ne:
ne
 only the extraordinary ray is transmitted
inserting the analyser  BLACK
no
Polariser
= EXTINCTION POSITION
Polariser parallel to no:
 only the ordinary ray is transmitted
inserting the analyser  BLACK
no
= EXTINCTION POSITION
ne
Diagonal position
Split into perpendicular two rays (vectors) :
1) ordinary ray where n = no
no
ne
Polariser
2) extraordinary ray where n = ne

Each ray has a N-S component, which are able
to pass through the analyser.

Maximum brightness is in the diagonal position.
As both rays are forced
to vibrate in the N-S direction,
they INTERFERE
So why do we see polarisation colours?
Retardation (Gangunterschied)
After time, t, when the slow ray is about to
emerge from the mineral:
 = retardation
Fast wave
with vf
(lower nf)
Slow wave
with vs
(higher ns)
d
Mineral
• The slow ray has travelled distance d…..
• The fast ray has travelled the distance d +
…..
Slow wave:
t = d/vs
Fast wave:
t = d/vf + /vair
…and so
d/vs = d/vf + /vair
 = d(vair/vs - vair/vf)
Polarised
light (E_W)
 = d(ns - nf)
 = d ∙ Δn
Retardation,  = d ∙ Δn (in nm)
Polariser
(E-W)
….and we know d (= 30m)….
Interference


Analyser forces rays to vibrate in
the N-S plane and interfere.
Destructive interference
(extinction):
 = k∙
k = 0, 1, 2, 3, …

Constructive interference
(maximum intensity):
 = (2k+1) ∙ /2
k = 0, 1, 2, 3, …
Explanation of interference colours
Example: a mineral with retardation of 550 nm in the diagonal position
Retardation, 
Wavelength, 
550
400
550
440
550
489
550
550
13/8 l
11/4 l
11/8 l
1l
550
629
550
733
7/
8
3/
4
l
 550 nm is lost, other wavelengths will be partly or fully transmitted.
l
Retardation, 
Wavelength, 
550
400
550
440
13/8 l
11/4 l 11/8 l
No green
(absorbed)
 red + violet
 purple
interference
colour
Fig 7-7 Bloss, Optical
Crystallography, MSA
550
489
550
550
1l
550
629
550
733
7/
3/
8
l
4
l
Retardation, 
Wavelength, 
800
400
800
426
800
457
800
550
800
581
800
711
2l
17/8 l
13/4 l
11/2 l
13/8 l
1 1/8 l 1 l
No red or
violet
(absorbed)
 green
interference
colour
Fig 7-7 Bloss, Optical
Crystallography, MSA
800
800
Michel-Lévy colour chart
Michel-Lévy colour chart
thickness of section
birefringence (d)
d = 0.009
d = 0.025
30 m
(0.03 mm)
retardation ()
first order
second order
third order
….orders separated by red colour bands….
Uniaxial indicatrix - summary






Can be positive or negative;
Mierals of the tetragonal, trigonal and hexagonal crystal
systems have a uniaxial indicatrix;
All sections apart from the basal section show a
polarisation colour;
All sections through the indicatrix contain nw;
The basal section is isotropic and means you are looking
down the c-axis of the crystal;
The principal section shows the maximum polarisation
colour characteristic for that mineral.
Polarisation colours






Isotropic (cubic) minerals show no birefringence and
remain black in XN;
Anisotropic minerals have variable n and therefore show
polarisation colours;
The larger n is, the higher the polarisation colour;
The polarisation colour is due to interference of rays of
different velocities;
THE MAXIMUM POLARISATION COLOUR IS THE
CHARACTERISTIC FEATURE OF A MINERAL (i.e., look
at lots of grains);
Polarisation colours should be reported with both
ORDER and COLOUR (e.g., second order blue, etc.).
Todays practical…..

Making the PPL observations you made in the previous 2
weeks;

Putting a scale on your sketches to estimate grain sizes;

Distinguishing isotropic from anisotropic minerals;

Calculating retardation;

Calculating and reporting birefringence - fringe counting.

Thinking about vibration directions….