Optical Mineralogy Wave Theory

= 2 X Amplitude Frequency = # of waves/sec to pass a given point (hz) f = v/ l v = velocity

Electromagnetic spectrum

Violet (400 nm)  & visible portion Red (700 nm) White = ROYGBV (can be separated by dispersion)

Refraction

Incident ray and reflected ray: 1)  of incidence i =  of reflection r' Incident i Reflected 2) coplanar “plane of incidence” (in plane ^ interface ) r’ air water r Refracted ray: 1) Slower in water (or glass) 2)  r   I Depends on D v Refracted

Index of refraction

For a substance x:

n

x = v air /v x

n

air = ??

light is slower in water, glass, crystals Is n water greater or less than 1??

Larger n associated with slower V !!

Snells Law: n i sin i = n r sin r for 2 known media (air/water) sin i/sin r = n r So can predict angle change!

/ n i = const

Polarization

Non-polarized (“usual”) light: Each photon vibrates as a wave form in a single plane Light beam = numerous photons, each vibrating in a different plane Vibration in all directions ~ perpendicular to propagation direction

Polarization

incoming ray is non-polarized reflected and refracted rays both become polarized

Polarization

Microscopes have two polarizers:  polarizer (below stage) is E-W  analyzer (above stage) is N-S

The Optical Indicatrix

Shows how n i varies with vibration direction.

Vectors radiating from center Length of each proportional to n i for light vibrating in the direction of the vector Indicatrix = surface connecting tips of vectors (a shape to represent changes in n with direction) Isotropic media have all n i the same (by definition) What is the shape of an isotropic indicatrix? a spherical indicatrix

North Fig. 6-6 P West P South A

The Optical Indicatrix

P A Fig 6-6 Bloss, Optical Crystallography, MSA P For isotropic minerals When analyzer inserted = crossed-nicols or XPL shorthand (vs PPL ) no light passes East  extinct , even when the stage is rotated

Anisotropic crystals

Calcite experiment and double refraction

Anisotropic crystals

Calcite experiment and double refraction

O E

Double images: Ray  2 rays with different propagation and vibration directions Each is polarized ( ^ each other) Fig 6-7 Bloss, Optical Crystallography, MSA

Anisotropic crystals

Calcite experiment and double refraction

O E

O-ray (Ordinary) Obeys Snell's Law and goes straight Vibrates ^ plane containing ray and c-axis ( “optic axis” ) Fig 6-7 Bloss, Optical Crystallography, MSA E-ray (Extraordinary) deflected Vibrates in plane containing ray and c-axis ..also doesn't vibrate ^ propagation, but we'll ignore this as we said earlier

O E

Fig 6-7 Bloss, Optical Crystallography, MSA IMPORTANT: A given ray of incoming light is restricted to only 2 (mutually perpendicular) vibration directions once it enters an anisotropic crystal Called privileged directions Each ray has a different n w = n o e = n E w < e (in the case of calcite)

n > 1 for all anisotropic substances n = f(vibration direction) Indicatrix no longer a sphere Indicatrix = ellipsoid Hexagonal and tetragonal xls have one unique xl axis (c axis) ^ 2 identical ones --UNIAXIAL MINERALS The optical properties reflect this as well: ellipsoid of rotation about c

Fig 6-10 Bloss, Optical Crystallography, MSA For light travelling parallel c, all vibration directions ^ c are the same:  circular section of indicatrix ( ^ c)  thus behaves as isotropic  only one (no unique plane containing ray and c-axis) ray (O-ray) with n = w ( doesn’t split to two rays)  extinct with analyzer in and stays that way as rotate stage

Fig. 6-12 For light travelling ^ c get elliptical principal section of indicatrix:  get 2 rays  O-ray with n = w  E-ray with n = e this e (parallel c) is the maximum possible deviation in n from w (true e) For random vibration direction  same situation as above Except that E-ray has some n between e and w All intermediate values are called e ’ (a variable value between e and w )

ellipsoid and conventions

:   (+) crystal = prolate e (-) crystal = oblate e > w < w Fig 6-11 Bloss, Optical Crystallography, MSA (-) crystal: w > e  oblate (+) crystal: e > w  prolate

Summary:

Fig. 6-12  Circular Section  ( ^ optic axis: all w 's)  extinct  Principal Sections  (have w and true e : max & n's) largest birefringence!

min  Random Sections ( e ' and w )  always have w !!

Any cut through center of a uniaxial indicatrix will have w as one

semiaxis

Color chart

Shows the relationship between retardation, crystal thickness, and interference color  550 m m  red violet  800 m m  green  1100 m m  red-violet again (note repeat  )  0-550 m m = “1 st order” 550-1100 m m = 2 nd order 1100-1650 m m = 3 rd order...

 Higher orders are more pastel

Example: Quartz w = 1.544 e = 1.553

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

Example: Quartz w = 1.544 e = 1.553

 Sign??

 e w (+) because e > w = 0.009 and is called the birefringence ( d ) = maximum interference color  What color is this?? 1) Follow line 0.009 in toward origin 2) Where it crosses 30 micron thickness (the standard for thin sections) we get a yellowish tan (see when quartz oriented with OA in plane of stage)  For other orientations get e ' w  progressively lower color Extinct when priv. direction N-S (every 90 o ) 360 o rotation  4 extinction positions exactly 90 o apart

Conoscopic Viewing

A condensing lens below the stage and a Bertrand lens above it Arrangement essentially folds planes of Fig 7-11  cone Fig 7-13 Bloss, Optical Crystallography, MSA Light rays are refracted by condensing lens & pass through crystal in different directions Thus different properties Only light in the center of field of view is vertical & like ortho  Interference Figures Very useful for determining optical properties of xl

Fig. 7-14

Uniaxial Figure

 Circles of isochromes  Note vibration directions:   w tangential e ' radial & variable magnitude  Black cross ( isogyres ) results from locus of extinction directions  Center of cross ( melatope ) represents optic axis  Approx 30 o inclination of OA will put it at margin of field of view

Fig. 7-14

Uniaxial Figure

 Centered axis figure as 7-14: when rotate stage cross does not rotate  Off center: cross still E-W and N-S, but melatope rotates around center  Melatope outside field: bars sweep through, but

always

N-S or E-W at center  Flash Figure : OA in plane of stage Diffuse black fills field brief time as rotate

Fig 8-1 Bloss, Optical Crystallography, MSA

Accessory Plates

 Use a 1st-order red (gypsum) plate  Slow direction is marked N on plate  Fast direction (n) || axis of plate  The gypsum crystal is oriented and cut so that D = (N-n)  550nm retardation  thus it has the effect of retarding the N ray 550 nm behind the n ray  If insert with no crystal on the stage  1 order red in whole field of view

n N

Accessory Plates

Suppose we view an anisotropic crystal with D = 100 nm (1-order gray) at 45 o from extinction If N gyp || N xl  Addition  Addition since ray in xl || N gyp  already behind by 100nm & it gets further retarded by 550nm in the gypsum plate  100 + 550  650nm   On your color chart what will result?

Original 1 o grey  2 o blue

Optic Sign Determination

For all xls remember e ' vibrates in and OA, w vibr normal to plane of ray plane of ray and OA

O E

e ' w e ' w e ' w e ' w (+) e ’ crystals: > so w w faster 1) Find a uniaxial crystal in which the optic axis (OA) is vertical (normal to the stage) How?

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

Fig 7-13 Bloss, Optical Crystallography, MSA

Optic Sign Determination

w e ' sub add e ' w e ' add w sub e ' w (+) e ’ crystals: > so w w faster Inserting plate for a (+) crystal:  subtraction in NW & SE where n||N  addition in NE & SW where N||N Whole NE (& SW) quads add 550nm  isochromes shift up 1 order Isogyre adds  red In NW & SE where subtract  Each isochrome loses an order Near isogyre (~100nm)  get yellow in NW & SE  and blue in NE & SW

(+) OA Figure without plate (+) OA Figure with plate Yellow in NW is (+)

(-) OA Figure without plate (same as (+) figure) (-) OA Figure with plate Blue in NW is (-)

Estimating birefringence

1) Find the crystal of interest showing the highest colors ( D depends on orientation) 2) Go to color chart thickness = 30 microns (but slides can be thick!) use 30 micron line + color, follow radial line through intersection to margin & read birefringence Suppose you have a mineral with second-order green What about third order yellow?

Pleochroism

 Changes in absorption color in PPL as rotate stage (common in biotite, amphibole…)  Pleochroic formula:  Tourmaline: e = dark green to bluish w = colorless to tan  Can determine this as just described by isolating first w and then e E-W and observing the color

Biaxial Crystals

Orthorhombic, Monoclinic, and Triclinic xls don't have 2 or more identical crystallographic axes  The indicatrix is a general ellipsoid with three unequal, mutually perpendicular axes  One is the smallest possible n and one the largest Fig 10-1 Bloss, Optical Crystallography, MSA a b g = smallest n = intermediate n = largest n (fastest) (slowest) The principal vibration directions are x , y , and z ( x || a , y || b , z || g ) By definition a < a ' < b < g '< g

g

Biaxial Crystals

If a < b < g between a then there must be some point & g with n = b Because =b in plane, and true b is normal to plane, then the section containing both is a circular section = b a Has all of the properties of a circular section! If look down it:  all rays = b  no preferred vibration direction  polarized incoming light will remain so  thus appear isotropic as rotate stage Looking down true b

OA g = b a

Biaxial Crystals

If a < b < g then there must be some point between a & g with n = b ^ optic axis by definition Looking down true b

OA g OA

Biaxial Crystals

If a < b < g then there must be some point between a & g with n = b ^ optic axis by definition And there must be two!  Biaxial = b a = b Hexagonal and tetragonal are Uniaxial Looking down true b

Biaxial Crystals

Nomenclature

:   2 circular sections  2 optic axes Must be in a g plane = Optic Axial Plane ( OAP ) Y || b direction ^ Fig 10-2 Bloss, Optical Crystallography, MSA • Acute angle between OA's = 2V OAP = optic normal • The axis that bisects acute angle = acute bisectrix = B xa • The axis that bisects obtuse angle = obtuse bisectrix = B xo

OA g OA

Biaxial Crystals

B(+) defined as Z ( g ) = B xa Thus b closer to a than to g = b a = b Looking down true b

g = b

Biaxial Crystals

B(-) defined as X ( a ) = B xa Thus b closer to g than to a OA a OA = b Looking down true b

Biaxial Interference Figures

Fig 10-15 Bloss, Optical Crystallography, MSA B xa figure Result is this pattern of isochromes for biaxial crystals

Biaxial Interference Figures Centered B

xa

Figure

Fig 10-16 Bloss, Optical Crystallography, MSA

Biaxial Interference Figures

Same figure rotated 45 o Optic axes are now E-W Clearly isogyres must swing Fig 10-16B Bloss, Optical Crystallography, MSA

As rotate Centered Optic Axis Figure Large 2V: Not much curvature B xa Figure with Small 2V:

B(-)

add

Biaxial Optic Sign

a

= B

xa

thus

b

closer to

g 100 gray + 550  650 blue subtract add 100 gray - 550  450 yellow Fig. 11-1A

B(-) Biaxial Optic Sign

a

= B

xa

thus

b

closer to

g

(in stage)

add Centered B xa 2V = 35 o subtract add Centered B xa 2V = 35 With accessory plate o

Biaxial Optic Sign B(+)

g

= B

xa

thus

b

closer to

a

(in stage)

sub add sub Fig. 11-1A

Estimating 2V

OAP Fig 11-5A Bloss, Optical Crystallography, MSA