Optical Mineralogy

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Optical Mineralogy

• Optical Indicatrix
• and Interference Figures

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Optical Indicatrix and Interference Figures LAB
TS-3 Uniaxial minerals Interference
figures Optic sign Pleochroic scheme LAB
TS-4 Biaxial minerals Interference
figures Optic sign Pleochroic scheme
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• Optical Indicatrix and Interference Figures
• Optical Indicatrix
• Uniaxial Interference Figures
• Biaxial Interference Figures

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Polarisation in the petrographic microscope
upper polarising filter (analyser)
what happens here??? LAB TS-2
sensitive tint plate
what happens here??? LAB TS-1
mineral sample (thin section)
conoscopic light
what happens here??? LAB TS-3,4
condenser lens
plane polarised light (PPL)
lower polarising filter (polariser)
unpolarised light
light source
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Optical Indicatrix Nesse, Ch. 7, p. 130-136
1. What is it?
a geometric figure that shows the index of
refraction and vibration direction for light
passing in any direction through a material
nmax (slow)
in 2D
nmin nmax
circle isotropic
nmin (fast)
nmin lt nmax
nmin
ellipse anisotropic
nmax
constructed as a sphere or ellipsoid with radii
parallel to the principal vibration directions
and lengths of axes proportional to refractive
index
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Optical Indicatrix
constructed as a sphere or ellipsoid with radii
parallel to the principal vibration directions
and lengths of axes proportional to refractive
index
nmax (slow)
in 2D
nmin nmax
circle isotropic
nmin (fast)
nmin lt nmax
nmin
ellipse anisotropic
nmax
in 3D indicatrix for isotropic mineral is a
sphere (of no further interest) indicatrix for
anisotropic mineral is an ellipsoid 2 cases
uniaxial and biaxial
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Optical Indicatrix
in 3D indicatrix for anisotropic mineral is an
ellipsoid
Z
random section
principal sections
WN
X
Y
ray paths tangent to indicatrix
wave normal propagation direction (incident PPL)
X lt Y lt Z (nfast lt nint lt nslow)
Nesse, 2000 Fig. 7.22
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Wave fronts
ray paths not necessarily // wave normal
Nesse, 2000 Fig. 7.2 d, e
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Case 1 Uniaxial minerals (hexagonal,
tetragonal a1 a2 c) principal axes ne
// c nw // a e extraordinary ray w
ordinary ray
X Y lt Z
X lt Y Z
Nesse, 2000 Fig. 7.23
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Case 1 Uniaxial minerals (hexagonal,
tetragonal a1 a2 c) principal axes ne
// c nw // a e extraordinary ray w
ordinary ray
X Y lt Z
X lt Y Z
Nesse, 2000 Fig. 7.23
X-Y plane circular section (all planes
perpendicular to Z) Z optic axis (c-axis
slow) ne gt nw ve
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Case 1 Uniaxial minerals (hexagonal,
tetragonal a1 a2 c) principal axes ne
// c nw // a e extraordinary ray w
ordinary ray
X Y lt Z
X lt Y Z
Nesse, 2000 Fig. 7.23
Y-Z plane circular section (all planes
perpendicular to X) X optic axis (c-axis
fast) ne lt nw -ve
X-Y plane circular section (all planes
perpendicular to Z) Z optic axis (c-axis
slow) ne gt nw ve
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Case 1 Uniaxial minerals (hexagonal,
tetragonal a1 a2 c) principal axes ne
// c nw // a e extraordinary ray w
ordinary ray
optic axis // plane of section plane of section
contains both nw and ne maximum d
Nesse, 2000 Fig. 7.25
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Case 1 Uniaxial minerals (hexagonal,
tetragonal a1 a2 c) principal axes ne
// c nw // a e extraordinary ray w
ordinary ray
optic axis // plane of section plane of section
contains both nw and ne maximum d
optic axis I plane of section plane of section
contains only nw minimum d (extinct!)
Nesse, 2000 Fig. 7.25
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Case 1 Uniaxial minerals (hexagonal,
tetragonal a1 a2 c) principal axes ne
// c nw // a e extraordinary ray w
ordinary ray
optic axis // plane of section plane of section
contains both nw and ne maximum d
random section contains nw and ne lt
ne intermediate d
optic axis I plane of section plane of section
contains only nw minimum d (extinct!)
Nesse, 2000 Fig. 7.25
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Optical Indicatrix and Symmetry
isometric system a1 a2 a3 all angles
90o indicatrix is a sphere minerals extinct in
XN hexagonal, trigonal, tetragonal systems a1
a2 ( a3) c all angles either 90o or
120o uniaxial indicatrix is ellipsoid X lt Y lt
Z c-axis optic axis e (either X or Z)
parallel extinction
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Case 2 Biaxial minerals (orthorhombic,
monoclinic, triclinic
systems a lt b lt c) indicatrix is
ellipsoid with axes X lt Y lt Z na // X, nb // Y,
ng // Z
Z
2V
only 2 circular sections possible
X
2 optic axes (OA) normal to the circular
sections acute angle between OA 2V
Y
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Case 2 Biaxial indicatrix ellipsoid with axes X
lt Y lt Z na // X, nb // Y, ng // Z
2 optic axes (OA) normal to the 2 circular
sections acute angle between OA 2V line
bisecting 2V Bxa acute bisectrix
2V
2V
where Bxa // Z ve where Bxa // X -ve
Nesse, 2000 Fig. 7.27
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random section oblique to both X-Z and circular
sections intermediate d
Case 2 Biaxial indicatrix ellipsoid with axes X
lt Y lt Z na // X, nb // Y, ng // Z
X-Z plane // plane of section plane of section
contains both na and ng maximum d
Nesse, 2000 Fig. 7.29
circular section // plane of section plane of
section I one OA minimum d (extinct!)
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Optic Sign
Case 1 Uniaxial minerals Z optic axis
(c-axis slow) ne gt nw ve X optic axis
(c-axis fast) ne lt nw -ve
Case 2 Biaxial minerals ve where Bxa //
Z -ve where Bxa // X
Z
Z
c OA Z
ve
-ve
ve
-ve
c OA X
X
X
a
a
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Optic Sign how do we figure this out???
Case 1 Uniaxial minerals Z optic axis
(c-axis slow) ne gt nw ve X optic axis
(c-axis fast) ne lt nw -ve
Case 2 Biaxial minerals ve where Bxa //
Z -ve where Bxa // X
Z
Z
c OA Z
ve
-ve
ve
-ve
c OA X
X
X
a
a
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Optic Sign how do we figure this out???
Requires conoscopic light (condenser lens in
place) interference figures (viewed with
Bertrand lens) use of STP to determine fast and
slow directions Nesse, Ch. 7, p. 139 -143
(uniaxial) p. 143 - 151
(biaxial)
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Extinction Angles
inclined (most biaxial)
parallel (uniaxial, some biaxial)
symmetrical (some uniaxial, some biaxial)
cant tell no prominent reference direction (uni
axial or biaxial)
Nesse, 2000 Fig. 7.32
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Extinction Angles
where optic axis is normal to plane of thin
section mineral will appear extinct for full
stage rotation! applies to both uniaxial and
biaxial minerals how distinguished from
isotropic minerals?
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Extinction Angles
where optic axis is normal to plane of thin
section mineral will appear extinct for full
stage rotation! applies to both uniaxial and
biaxial minerals how distinguished from
isotropic minerals? (also requires interference
figures stay tuned.....)
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Optical Indicatrix and Symmetry
isometric system a1 a2 a3 all angles
90o indicatrix is a sphere minerals extinct in
XN hexagonal, trigonal, tetragonal systems a1
a2 ( a3) c all angles either 90o or
120o uniaxial indicatrix is ellipsoid X lt Y lt
Z c-axis optic axis e (either X or Z)
parallel extinction orthorhombic system a
b c all angles 90o biaxial indicatrix is
ellipsoid X lt Y lt Z X, Y, Z //
crystallographic axes 2 circular sections I
2 optic axes parallel extinction
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Optical Indicatrix and Symmetry
orthorhombic system a b c all angles
90o biaxial indicatrix is ellipsoid X lt Y lt
Z X, Y, Z ? crystallographic axes 2
circular sections I 2 optic axes parallel
extinction monoclinic system a b c a g
90o b 90o biaxial indicatrix is ellipsoid
X lt Y lt Z one of X, Y, Z ? one
crystallographic axis inclined
extinction triclinic system a b c a b
g 90o biaxial indicatrix is ellipsoid X lt Y
lt Z no correspondence X, Y, Z ? cryst.
axes inclined extinction
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Optic Sign Summary
Case 1 Uniaxial minerals Z optic axis
(c-axis slow) ne gt nw ve X optic axis
(c-axis fast) ne lt nw -ve
Case 2 Biaxial minerals ve where Bxa //
Z -ve where Bxa // X
Z
Z
c OA Z
ve
-ve
ve
-ve
c OA X
X
Bxa
X
a
a
Bxa
determined from OA figure
determined from Bxa or OA figure