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Today’s objectivesToday’s objectives• What happens when light passes through What happens when light passes through

most minerals?most minerals?• Why do some minerals change color when Why do some minerals change color when

the microscope stage is rotated (without the microscope stage is rotated (without analyzer)?analyzer)?

• What causes the colors you saw when you What causes the colors you saw when you inserted the analyzer?inserted the analyzer?

• Why do those colors go to black every 90 Why do those colors go to black every 90 degrees of rotation?degrees of rotation?

• How can we use those colors to help us How can we use those colors to help us identify unknown minerals?identify unknown minerals?

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BackgroundBackground

• VectorsVectors

• Light as waveLight as wave

• Interference (2D)Interference (2D)

• Interference (3D)Interference (3D)

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PolarizationPolarization

• Light can be constrained to vibrate in a Light can be constrained to vibrate in a particular planeparticular plane

• When two light rays combine, their When two light rays combine, their vibration vectors add (vector-wise)vibration vectors add (vector-wise)

A

B

C

A+B=C

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PolarizationPolarization

• Polaroid film (in the polarizer & analyzer Polaroid film (in the polarizer & analyzer on your scope) absorbs light vibrating on your scope) absorbs light vibrating perpendicular to it’s directionperpendicular to it’s direction

incoming ray

polarizer direction

transmitted component

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Anisotropic materialsAnisotropic materials

• Cause light to split into 2 rays vibrating Cause light to split into 2 rays vibrating 90° to each other90° to each other

• Two rays “see” a different crystal Two rays “see” a different crystal environmentenvironment– different indices of refractiondifferent indices of refraction

• different speeds of lightdifferent speeds of light

– different pathsdifferent paths• produces double refractionproduces double refraction

polarized

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Double refractionDouble refraction

• Calcite demoCalcite demo– One ray takes unexpected path through One ray takes unexpected path through

crystal (extraordinary, crystal (extraordinary, ´ or E´ ray)´ or E´ ray)

– Special direction where this doesn’t Special direction where this doesn’t happen: optic axishappen: optic axis

– calcite ncalcite n = 1.658 and n = 1.658 and n´́ = 1.486 = 1.486

– which image looks “deeper”?which image looks “deeper”?

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QuickTime™ and aSorenson Video 3 decompressorare needed to see this picture.

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PleochroismPleochroism• Two rays are Two rays are

absorbed differentlyabsorbed differently– can show different can show different

color (distribution of color (distribution of wavelengths)wavelengths)

– or intensity of coloror intensity of color

fast ray

slow ray

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PleochroismPleochroism• Isometric - no pleo.Isometric - no pleo.• Hexagonal, Hexagonal,

tetragonal - 2 “end-tetragonal - 2 “end-member” colorsmember” colors

• Triclinic, Monoclinic, Triclinic, Monoclinic, Orthorhombic - 3 Orthorhombic - 3 “end-members”“end-members”

QuickTime™ and aSorenson Video 3 decompressorare needed to see this picture.

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PleochroismPleochroism• Isometric - no pleo.Isometric - no pleo.• Hexagonal, Hexagonal,

tetragonal - 2 “end-tetragonal - 2 “end-member” colorsmember” colors

• Triclinic, Monoclinic, Triclinic, Monoclinic, Orthorhombic - 3 Orthorhombic - 3 “end-members”“end-members”

QuickTime™ and aVideo decompressor

are needed to see this picture.

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Recap - PleochroismRecap - Pleochroism

• Anisotropic grain has fast and slow Anisotropic grain has fast and slow directionsdirections

• In some minerals, these show different In some minerals, these show different colorscolors

• Because the incoming light is polarized, Because the incoming light is polarized, when one ray is perpendicular to that when one ray is perpendicular to that direction, it is excluded and the other direction, it is excluded and the other color is displayedcolor is displayed

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monochromatic!

RetardationRetardation• fast & slow rays are fast & slow rays are

45° from polarizer45° from polarizer

• = d (n= d (nss - n - nff))– distance, nmdistance, nm 1

1.5

fast

slow

=/2

d

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InterferenceInterference• Retarded rays get Retarded rays get

vector-combined in vector-combined in analyzer (“XP”)analyzer (“XP”)

fast

slow

=/2

Retardation of Retardation of /2 /2 causes change in causes change in

vibration direction of vibration direction of 90° (full transmission)90° (full transmission)

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InterferenceInterference• If If =n=n (n=1,2,3...)(n=1,2,3...), no , no

ray passes analyzerray passes analyzer

Retardation of Retardation of causes change in causes change in

vibration direction of vibration direction of 180° (no transmission)180° (no transmission)

fast

slow

=

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Recap: Retardation / Recap: Retardation / InterferenceInterference

• The slow ray is held back, so at the analyzer The slow ray is held back, so at the analyzer they combine with a new net vibration direction they combine with a new net vibration direction ((retardation changes vibration directionretardation changes vibration direction))

• The relationship between the retardation The relationship between the retardation distance, grain thickness, and indices of distance, grain thickness, and indices of refraction is:refraction is:– = d (n= d (nss - n - nff))

• If the new vibration direction is 0° or 180° from If the new vibration direction is 0° or 180° from the incoming, the ray is canceled at the the incoming, the ray is canceled at the analyzer (upper polar)analyzer (upper polar)– when when ==, or , or =2=2, or , or =3=3, or , or =4=4, etc., etc.

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• When fast or slow When fast or slow direction || polarizerdirection || polarizer– will occur every 90° will occur every 90°

of stage rotationof stage rotation

• Calcite demoCalcite demo fast

slow

ExtinctionExtinction

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monochromatic!

Interference ColorsInterference Colors• What changes for What changes for

other colors other colors (wavelengths)?(wavelengths)?

• = d (n= d (nss - n - nff)) 1

1.5

fast

slow

=/2

d

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Interference ColorsInterference Colors

• Story above was for one wavelength Story above was for one wavelength (color) of light(color) of light

• Retardation distance (Retardation distance () is ~same ) is ~same across colors, but:across colors, but:– = n = n -> no ray (rotation = 0° or 180°) -> no ray (rotation = 0° or 180°)– = [n = [n - ( - (/2)] -> max.ray (rot.=90°, 270°)/2)] -> max.ray (rot.=90°, 270°)

• Certain wavelengths get blocked at Certain wavelengths get blocked at analyzer, others passanalyzer, others pass– produces an “interference color”produces an “interference color”

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Thickness effectThickness effect

• = d (n= d (nss - n - nff))

• quartz wedge demoquartz wedge demo– = (n= (nss - n - nff) = 0.009 ) = 0.009

(a small value)(a small value)– shows change in set shows change in set

of transmitted of transmitted wavelengths (i.e., wavelengths (i.e., color) with increasing color) with increasing retardation, retardation,

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Birefringence effectBirefringence effect

• = d (n= d (nss - n - nff) = d ) = d – can get same set of colors by varying can get same set of colors by varying at at

constant dconstant d

• maximum maximum is characteristic of mineral! is characteristic of mineral!– e.g., calcite e.g., calcite = 0.172 (a large value) = 0.172 (a large value)

• orientation-dependentorientation-dependent– (=n(=nss-n-nff) ranges from 0 to a maximum) ranges from 0 to a maximum– 0 is looking down optic axis0 is looking down optic axis

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Interference Color ChartInterference Color Chartth

ickn

ess,

d (

µm

)

retardation, (nm)

birefringence,

birefringence,

quartz?

quartz?

• range of colors - same as quartz wedgerange of colors - same as quartz wedge

• measuring birefringencemeasuring birefringence

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Interference Color ChartInterference Color Chartth

ickn

ess,

d (

µm

)

retardation, (nm)

birefringence,

birefringence,

• OrdersOrders

• Every 550 nm (≈ Every 550 nm (≈ blueblue))

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Interference Color ChartInterference Color Chart

• Two kinds of whiteTwo kinds of white– low-orderlow-order– high-orderhigh-order

= 0.172

d = 30 µm

what color is out here?

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Next LectureNext Lecture• How do you know which “white” you’re How do you know which “white” you’re

looking at?looking at?– Wedge effect, gypsum plateWedge effect, gypsum plate

• Mineral ID features: sign of elongation, Mineral ID features: sign of elongation, extinction type/angleextinction type/angle

• Which is the slow ray, Which is the slow ray, or or ? ?– Uniaxial indicatrix, conoscopic illuminationUniaxial indicatrix, conoscopic illumination

• How are biaxial minerals different?How are biaxial minerals different?– Biaxial indicatrix, conoscopic illuminationBiaxial indicatrix, conoscopic illumination

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Questions to think aboutQuestions to think about

• How many pleochroic colors would a How many pleochroic colors would a mineral show that stayed black in XP?mineral show that stayed black in XP?

• Before polarizing film, microscopes Before polarizing film, microscopes used a Nicol prism, made of two used a Nicol prism, made of two specially-cut pieces of calcite, glued specially-cut pieces of calcite, glued together. How could you cut calcite to together. How could you cut calcite to make this work?make this work?

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fastslow

550 nm

Accessory platesAccessory plates• Tell you fast vs. slow Tell you fast vs. slow

directionsdirections– Fig. 7.21, p. 129Fig. 7.21, p. 129

• Can add or subtract Can add or subtract retardation:retardation:– Gypsum plate has Gypsum plate has

= 550 nm (“= 550 nm (“”)”)– Mica plate has Mica plate has = =

138 nm (“138 nm (“/4”)/4”)

• Short dimension is Short dimension is always slowalways slow

100 nm

450 nm

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Accessory platesAccessory plates• Tell you fast vs. slow Tell you fast vs. slow

directionsdirections– Fig. 7.21, p. 129Fig. 7.21, p. 129

• Can add or subtract Can add or subtract retardation:retardation:– Gypsum plate has Gypsum plate has

= 550 nm (“= 550 nm (“”)”)– Mica plate has Mica plate has = =

138 nm (“138 nm (“/4”)/4”)

• Short dimension is Short dimension is always slowalways slow

100 nm

650 nm

fastslow

550 nm

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Using accessory platesUsing accessory plates• 1) Find vibration 1) Find vibration

directions, using directions, using extinctionextinction

• 2) Rotate so 2) Rotate so vibration directions vibration directions are “diagonal”are “diagonal”

• 3) Insert plate3) Insert plate• 4) If colors “add”, 4) If colors “add”,

slowslowmineralmineral || slow || slowplateplate, , otherwise, slowotherwise, slowmineralmineral || fast|| fastplateplate

XP

=200 nm

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Using accessory platesUsing accessory plates• 1) Find vibration 1) Find vibration

directions, using directions, using extinctionextinction

• 2) Rotate so 2) Rotate so vibration directions vibration directions are “diagonal”are “diagonal”

• 3) Insert plate3) Insert plate• 4) If colors “add”, 4) If colors “add”,

slowslowmineralmineral || slow || slowplateplate, , otherwise, slowotherwise, slowmineralmineral || fast|| fastplateplate

p

q

XP

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Using accessory platesUsing accessory plates• 1) Find vibration 1) Find vibration

directions, using directions, using extinctionextinction

• 2) Rotate so 2) Rotate so vibration directions vibration directions are “diagonal”are “diagonal”

• 3) Insert plate3) Insert plate• 4) If colors “add”, 4) If colors “add”,

slowslowmineralmineral || slow || slowplateplate, , otherwise, slowotherwise, slowmineralmineral || fast|| fastplateplate

pp

qq

XP45°

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Using accessory platesUsing accessory plates• 1) Find vibration 1) Find vibration

directions, using directions, using extinctionextinction

• 2) Rotate so 2) Rotate so vibration directions vibration directions are “diagonal”are “diagonal”

• 3) Insert plate3) Insert plate• 4) If colors “add”, 4) If colors “add”,

slowslowmineralmineral || slow || slowplateplate, , otherwise, slowotherwise, slowmineralmineral || fast|| fastplateplate

pp

qq

XP

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Using accessory platesUsing accessory plates• 1) Find vibration 1) Find vibration

directions, using directions, using extinctionextinction

• 2) Rotate so 2) Rotate so vibration directions vibration directions are “diagonal”are “diagonal”

• 3) Insert plate3) Insert plate• 4) If colors “add”, 4) If colors “add”,

slowslowmineralmineral || slow || slowplateplate, , otherwise, slowotherwise, slowmineralmineral || fast|| fastplateplate

pp

qq

XP

p =

slow

=750 nm