optical mineralogy wave theory = 2 x amplitude frequency = # of waves/sec to pass a given point (hz)...

Optical MineralogyOptical MineralogyWave TheoryWave Theory

= 2 X Amplitude = 2 X Amplitude

Frequency = # of waves/sec to pass a Frequency = # of waves/sec to pass a given point (hz)given point (hz)

f = v/f = v/ v = velocity v = velocity

Electromagnetic spectrumElectromagnetic spectrum & visible portion & visible portion

Violet (400 nm) Violet (400 nm) Red (700 nm) Red (700 nm)

White = ROYGBVWhite = ROYGBV(can be separated by (can be separated by dispersiondispersion))

RefractionRefractionIncidentIncident ray and ray and reflectedreflected ray: ray:

1) 1) of incidence i = of incidence i = of of reflection r'reflection r'

2) coplanar 2) coplanar “plane of incidence”“plane of incidence”

(in plane (in plane interfaceinterface))

RefractedRefracted ray: ray:1) Slower in water (or 1) Slower in water (or

glass)glass)

2) 2) r r I I

Depends on Depends on v v

IncidentIncident

ReflectedReflectedairair

RefractedRefracted

water

iir’r’

rr

Index of refractionIndex of refraction

For a substance x:For a substance x:nnxx = v = vairair/v/vxx

nnairair = ?? = ??

light is slower in water, glass, crystalslight is slower in water, glass, crystalsIs nIs nwaterwater greater or less than 1?? greater or less than 1??

Larger n associated with slower V !!Larger n associated with slower V !!

Snells Law:Snells Law: nnii sin i = n sin i = nrr sin r sin r

for 2 known media (air/water) sin i/sin r = nfor 2 known media (air/water) sin i/sin r = nrr / n / nii = const = const

So can predict angle change!So can predict angle change!

PolarizationPolarization

Non-polarized (“usual”) light:Non-polarized (“usual”) light:

Each photon vibrates as a wave form in a single planeEach photon vibrates as a wave form in a single plane

Light beam = numerous photons, each vibrating in a Light beam = numerous photons, each vibrating in a different planedifferent plane

Vibration in all directions ~ perpendicular to propagation Vibration in all directions ~ perpendicular to propagation directiondirection

PolarizationPolarization

reflected and refracted raysboth become polarized

incoming ray is non-polarized

PolarizationPolarizationMicroscopes have two polarizers:Microscopes have two polarizers: polarizerpolarizer (below stage) is E-W (below stage) is E-W analyzeranalyzer (above stage) is N-S (above stage) is N-S

The Optical IndicatrixThe Optical Indicatrix

Shows how nShows how nii varies with varies with vibrationvibration direction. direction.

Vectors radiating from centerVectors radiating from center

Length of each proportional to nLength of each proportional to nii for light for light vibratingvibrating in the direction of the in the direction of the

vectorvector

IndicatrixIndicatrix = surface connecting tips of vectors = surface connecting tips of vectors

(a shape to represent changes in n with direction)(a shape to represent changes in n with direction)

IsotropicIsotropic media have all n media have all nii the same (by definition) the same (by definition)

What is the shape of an isotropic indicatrix? What is the shape of an isotropic indicatrix?

a sphericala spherical indicatrix indicatrix

The Optical The Optical IndicatrixIndicatrix

For isotropic mineralsFor isotropic minerals

When analyzer inserted When analyzer inserted = = crossed-nicolscrossed-nicols or or XPLXPL shorthand (vs shorthand (vs PPLPPL) no light passes) no light passes

extinctextinct, even , even when the stage is when the stage is rotatedrotated

Fig. 6-6

East

West

North South

P P

PP

A

AFig 6-6 Bloss, Optical Crystallography, MSA

Anisotropic crystalsAnisotropic crystalsCalcite experiment and Calcite experiment and double refractiondouble refraction

Anisotropic crystalsAnisotropic crystalsCalcite experiment and Calcite experiment and double refractiondouble refraction

O E Double images:Double images:

Ray Ray 2 rays with 2 rays with different propagation different propagation and vibration directionsand vibration directions

Each is polarized ( Each is polarized ( each other)each other)

Fig 6-7 Bloss, Optical Crystallography, MSA

Anisotropic crystalsAnisotropic crystalsCalcite experiment and double refractionCalcite experiment and double refraction

O E O-ray (Ordinary) O-ray (Ordinary)

Obeys Snell's Law and goes Obeys Snell's Law and goes straightstraight

Vibrates Vibrates plane containing plane containing ray and c-axis (ray and c-axis (“optic axis”“optic axis”))

E-ray (Extraordinary)E-ray (Extraordinary)

deflecteddeflected

Vibrates Vibrates inin plane containing plane containing ray and c-axisray and c-axis

..also doesn't vibrate ..also doesn't vibrate propagation, but we'll ignore propagation, but we'll ignore this as we said earlierthis as we said earlier


O E


IMPORTANT: A given ray of IMPORTANT: A given ray of incoming light is restricted to only 2 incoming light is restricted to only 2 (mutually perpendicular) vibration (mutually perpendicular) vibration directions once it enters an directions once it enters an anisotropic crystalanisotropic crystal

Called Called privileged directionsprivileged directions

Each ray has a different nEach ray has a different n

= n= noo

= n= nEE

< < (in the case of calcite) (in the case of calcite)

n > 1 for all anisotropic substancesn > 1 for all anisotropic substances

n = f(vibration direction) n = f(vibration direction)

Indicatrix no longer a sphereIndicatrix no longer a sphere

Indicatrix = Indicatrix = ellipsoidellipsoid

Hexagonal and tetragonal xls have one unique xl axis (c Hexagonal and tetragonal xls have one unique xl axis (c axis) axis) 2 identical ones --UNIAXIAL MINERALS 2 identical ones --UNIAXIAL MINERALS

The optical properties reflect this as well: The optical properties reflect this as well: ellipsoid of ellipsoid of rotation about crotation about c

For light For light travelling travelling parallel c, all parallel c, all vibration vibration directions directions c are c are the same:the same:


circular sectioncircular section of indicatrix ( of indicatrix ( c) c)thus thus behaves as isotropicbehaves as isotropic

(no unique plane containing ray and c-axis)(no unique plane containing ray and c-axis)only only oneone ray (O-ray) with n = ray (O-ray) with n = doesn’t split to two rays)doesn’t split to two rays)extinctextinct with analyzer in and stays that way as rotate stage with analyzer in and stays that way as rotate stage

Fig. 6-12

For For random vibration directionrandom vibration direction same situation as above same situation as above

Except that E-ray has some n between Except that E-ray has some n between and and

All intermediate values are called All intermediate values are called ’ ’ (a variable value between (a variable value between and and ))

For light travelling For light travelling c get c get elliptical elliptical principal sectionprincipal section of indicatrix: of indicatrix:

get 2 raysget 2 raysO-ray with n = O-ray with n = E-ray with n = E-ray with n = this this (parallel c) is the (parallel c) is the maximum possible deviation maximum possible deviation in n from in n from (true (true

ellipsoid and conventions: (+) crystal = prolate > (-) crystal = oblate <

(-) crystal: > oblate

(+) crystal: > prolate


Fig. 6-12

Summary:Summary: Circular SectionCircular Section (( optic axis: all optic axis: all 's)'s) extinctextinct

Principal Sections Principal Sections (have (have and true and true : max : max && min min n's) largest birefringence!n's) largest birefringence!

Random Sections (Random Sections (' and ' and ) ) always have always have !!!!

AnyAny cut through center of a cut through center of a uniaxial indicatrix will have uniaxial indicatrix will have as one as one semiaxissemiaxis

Color chartColor chart

Shows the relationship between retardation, crystal Shows the relationship between retardation, crystal

thickness, and interference colorthickness, and interference color

550 550 mm red violet red violet

800 800 mm green green

1100 1100 m m red-violet again (note repeat red-violet again (note repeat ))

0-550 0-550 m = “1m = “1stst order” 550-1100 order” 550-1100 m = 2m = 2ndnd

order 1100-1650 order 1100-1650 m = 3m = 3rd rd order...order...

Higher orders are more pastelHigher orders are more pastel

Example: Quartz Example: Quartz = 1.544 = 1.544 = 1.553 = 1.553

1.55

31.

553

1.5441.544

Data from Deer et al Rock Forming Minerals John Wiley & Sons

Example: Quartz Example: Quartz = 1.544 = 1.544 = 1.553 = 1.553

1.553

1.553

1.5441.544

Sign??Sign?? (+) (+) because because > > - - = 0.009 and is called the = 0.009 and is called the birefringence (birefringence ())

= = maximummaximum interference color interference color

What color is this?? What color is this??

1) Follow line 0.009 in toward origin1) Follow line 0.009 in toward origin

2) Where it crosses 30 micron thickness (the standard for thin 2) Where it crosses 30 micron thickness (the standard for thin

sections) we get a yellowish tan (see when quartz oriented with OA sections) we get a yellowish tan (see when quartz oriented with OA

in plane of stage)in plane of stage)

For other orientations get For other orientations get ' - ' - progressively lower progressively lower

colorcolor

Extinct when priv. direction N-S (every 90Extinct when priv. direction N-S (every 90oo) )

360360oo rotation rotation 4 extinction positions 4 extinction positions exactlyexactly 90 90oo apart apart

Conoscopic ViewingConoscopic ViewingA A condensing lenscondensing lens below the stage and a below the stage and a Bertrand Bertrand

lenslens above it above itArrangement essentially folds planes of Fig 7-11 Arrangement essentially folds planes of Fig 7-11 cone cone


Light rays are refracted by Light rays are refracted by condensing lens & pass condensing lens & pass through crystal in through crystal in different different directionsdirections

Thus different Thus different propertiesproperties

Only light in the center of field Only light in the center of field of view is vertical & like orthoof view is vertical & like ortho

Interference FiguresInterference Figures Very Very useful for determining optical useful for determining optical properties of xlproperties of xl

Uniaxial FigureUniaxial Figure

Circles of Circles of isochromesisochromes

Note vibration directions: Note vibration directions:

tangential tangential

' radial & variable magnitude' radial & variable magnitude

Black cross (Black cross (isogyresisogyres) results from locus ) results from locus

of extinction directionsof extinction directions

Center of cross (Center of cross (melatopemelatope) represents ) represents

optic axisoptic axis

Approx 30Approx 30oo inclination of OA will put it inclination of OA will put it

at margin of field of viewat margin of field of view

Fig. 7-14Fig. 7-14

Uniaxial FigureUniaxial Figure

Fig. 7-14Fig. 7-14

Centered axis figure as 7-14: when Centered axis figure as 7-14: when

rotate stage cross does rotate stage cross does notnot rotate rotate

Off center: cross still E-W and N-S, but Off center: cross still E-W and N-S, but

melatope rotates around centermelatope rotates around center

Melatope outside field: bars sweep Melatope outside field: bars sweep

through, but through, but alwaysalways N-S or E-W at center N-S or E-W at center

Flash FigureFlash Figure: OA in plane of stage : OA in plane of stage

Diffuse black fills field brief time as Diffuse black fills field brief time as

rotaterotate

Accessory PlatesAccessory Plates Use a 1st-order red (gypsum) plateUse a 1st-order red (gypsum) plate

Slow direction is marked Slow direction is marked NN on plate on plate

Fast direction (n) || axis of plateFast direction (n) || axis of plate

The gypsum crystal is oriented and cut so that The gypsum crystal is oriented and cut so that = (N-n) = (N-n) 550nm retardation 550nm retardation

thus it has the effect of retarding the N ray thus it has the effect of retarding the N ray 550 nm behind the n ray550 nm behind the n ray

If insert with no crystal on the stage If insert with no crystal on the stage 1- 1-order red in whole field of vieworder red in whole field of view


Accessory PlatesAccessory PlatesSuppose we view an anisotropic crystal with Suppose we view an anisotropic crystal with

= 100 nm (1-order gray) at 45 = 100 nm (1-order gray) at 45oo from extinction from extinction

NN

NNnn

If NIf Ngypgyp || N || Nxlxl AdditionAddition

Addition since ray in xl || NAddition since ray in xl || Ngypgyp already behind by 100nm & it gets already behind by 100nm & it gets further retardedfurther retarded by 550nm in the by 550nm in the gypsum plategypsum plate100 + 550 100 + 550 650nm 650nmOn your color chart what will On your color chart what will result?result?Original 1Original 1oo grey grey 2 2oo blue blue

Optic Sign DeterminationOptic Sign DeterminationFor For allall xls remember xls remember ' vibrates ' vibrates inin plane of ray plane of ray

and OA, and OA, vibr vibr normal tonormal to plane of ray and OA plane of ray and OA

1) Find a uniaxial crystal in which the optic 1) Find a uniaxial crystal in which the optic axis (OA) is vertical (normal to the stage) axis (OA) is vertical (normal to the stage) How?How?

2) Go to high power, insert condensing and 2) Go to high power, insert condensing and Bertrand lenses to Bertrand lenses to optic axis interference optic axis interference figurefigure

' '

''

(+) crystals: ’ > so faster

O E

Optic Sign DeterminationOptic Sign Determination

NN

(+) crystals: ’ > so faster

' '

''

add

add

sub

sub

Inserting plate for a (+) crystal:Inserting plate for a (+) crystal:

subtraction in NW & SE where n||Nsubtraction in NW & SE where n||N

addition in NE & SW where N||Naddition in NE & SW where N||N

Whole NE (& SW) quads add 550nmWhole NE (& SW) quads add 550nm

isochromes shift up 1 orderisochromes shift up 1 order

Isogyre adds Isogyre adds red red

In NW & SE where subtractIn NW & SE where subtract

Each isochrome loses an order Each isochrome loses an order

Near isogyre (~100nm) Near isogyre (~100nm)

get yellow in NW & SE get yellow in NW & SE

and blue in NE & SWand blue in NE & SW

(+) OA Figure with plate(+) OA Figure with plateYellow in NW is (+)Yellow in NW is (+)

(+) OA Figure without plate(+) OA Figure without plate

(-) OA Figure with plate(-) OA Figure with plateBlue in NW is (-)Blue in NW is (-)

(-) OA Figure without plate(-) OA Figure without plate(same as (+) figure)(same as (+) figure)

Estimating birefringenceEstimating birefringence

1)1) Find the crystal of interest showing the Find the crystal of interest showing the highest colors (highest colors ( depends on orientation) depends on orientation)

2)2) Go to color chart Go to color chartthickness = 30 microns (but slides can be thick!)thickness = 30 microns (but slides can be thick!)

use 30 micron line + color, follow radial line through use 30 micron line + color, follow radial line through intersection to margin & read birefringenceintersection to margin & read birefringence

Suppose you have a mineral with second-order greenSuppose you have a mineral with second-order green

What about third order yellow?What about third order yellow?

PleochroismPleochroism

Changes in absorption color Changes in absorption color in PPLin PPL as as rotate stage (common in biotite, rotate stage (common in biotite, amphibole…)amphibole…)Pleochroic formula:Pleochroic formula:

Tourmaline: Tourmaline: = dark green to bluish = dark green to bluish

= colorless to tan = colorless to tanCan determine this as just described by Can determine this as just described by isolating first isolating first and then and then E-W and E-W and observing the colorobserving the color

Biaxial CrystalsBiaxial CrystalsOrthorhombic, Monoclinic, and Triclinic xls don't have Orthorhombic, Monoclinic, and Triclinic xls don't have

2 or more identical crystallographic axes2 or more identical crystallographic axes The indicatrix is a general ellipsoid with three unequal, The indicatrix is a general ellipsoid with three unequal,

mutually perpendicular axesmutually perpendicular axes One is the smallest possible n and one the largestOne is the smallest possible n and one the largest

= smallest n= smallest n (fastest)(fastest) = intermediate n= intermediate n = largest n= largest n (slowest)(slowest)

The The principal vibration directionsprincipal vibration directions are are xx, , yy, and , and zz ( x || ( x || , y || , y || , z || , z || ))

By definition By definition ' < ' < '< '<


Biaxial CrystalsBiaxial Crystals

Looking down trueLooking down true

= =

If < < then there must be some point between & with n = Because =b in plane, and true b is normal to plane, then the section containing both is a circular section

Has all of the properties of a circular section! If look down it:

all rays = no preferred vibration directionpolarized incoming light will remain sothus appear isotropic as rotate stage

Biaxial CrystalsBiaxial CrystalsIf < < then there must be some point

between & with n =


= =

optic axis by definition

OAOA

Biaxial CrystalsBiaxial CrystalsIf < < then there must be some point

between & with n =


= =

= =

optic axis by definition

And there must be two! Biaxial

Hexagonal and tetragonal are Uniaxial

OAOA OAOA

Biaxial CrystalsBiaxial CrystalsNomenclatureNomenclature:: 2 circular sections 2 circular sections

2 optic axes 2 optic axes Must be in Must be in -- plane = plane = Optic Axial Optic Axial Plane Plane ((OAPOAP))

Y || Y || direction direction OAP = OAP = optic normaloptic normal


•Acute angle between OA's = 2VAcute angle between OA's = 2V

•The axis that bisects acute angle = The axis that bisects acute angle = acute bisectrixacute bisectrix = B= Bxaxa

•The axis that bisects obtuse angle = The axis that bisects obtuse angle = obtuse bisectrix = Bobtuse bisectrix = Bxoxo

Biaxial CrystalsBiaxial CrystalsB(+)B(+) defined as Z ( defined as Z () = B) = Bxa xa

Thus Thus closer to closer to than to than to


= =

= =

OAOA OAOA

Biaxial CrystalsBiaxial CrystalsB(-) defined as X () = Bxa

Thus closer to than to


= =

= =

OAOA

OAOA

Biaxial Interference FiguresBiaxial Interference Figures

BBxaxa figure figure

Result is this pattern Result is this pattern of isochromes for of isochromes for biaxial crystalsbiaxial crystals


Biaxial Interference FiguresBiaxial Interference FiguresCentered BCentered Bxaxa Figure Figure


Biaxial Interference FiguresBiaxial Interference Figures

Same figure rotated 45Same figure rotated 45oo

Optic axes are now E-WOptic axes are now E-W

Clearly isogyres must swingClearly isogyres must swing

Fig 10-16B Bloss, Optical Crystallography, MSA

As rotate

Centered Optic Axis Figure Large 2V:

Bxa Figure with Small 2V:

Not much Not much curvaturecurvature

Biaxial Optic SignBiaxial Optic Sign

B(-)B(-) = B = Bxaxa thus thus closer to closer to

Fig. 11-1A

addadd

addadd

subtractsubtract

100 gray + 550 100 gray + 550 650 blue 650 blue

100 gray - 550 100 gray - 550 450 yellow 450 yellow


B(-)B(-) = B = Bxaxa thus thus closer to closer to (in stage) (in stage)

addadd

subtractsubtract

addadd

Centered BCentered Bxaxa 2V = 35 2V = 35oo Centered BCentered Bxaxa 2V = 35 2V = 35oo

With accessory plateWith accessory plate


B(+)B(+) = B = Bxaxa thus thus closer to closer to (in stage) (in stage)

Fig. 11-1A

subsub

subsub

addadd

Estimating 2VEstimating 2V

OAPOAPFig 11-5A Bloss, Optical Crystallography, MSA

optical mineralogy wave theory = 2 x amplitude frequency = # of waves/sec to pass a given point (hz)...

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optical crystallography

given ray of incoming

light vibrating

optical mineralogywave