frequency = # of waves/sec to pass a given point (hz)
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Frequency = # of waves/sec to pass a given point (hz)
Optical Mineralogy Wave Theory = 2 X Amplitude Frequency = # of
waves/sec to pass a given point (hz) f = v/l v = velocity
Electromagnetic spectrum & visible portion
Violet (400 nm) Red (700 nm) White = ROYGBV (can be separated by
dispersion) Refraction Incident ray and reflected ray: Refracted
ray:
1) of incidence i = of reflection r' 2) coplanar plane of incidence
(in plane ^ interface) Refracted ray: 1) Slower in water(or glass)
2) r I Depends on D v Incident i Reflected r air water r Refracted
Index of refraction For a substance x: nx = vair/vx nair =
Index of refraction For a substance x: nx = vair/vx nair = ??light
is slower in water, glass, crystals Is nwatergreater or less than
1?? Larger n associated with slower V !!Snells Law: ni sin i = nr
sin r for 2 known media (air/water) sin i/sin r = nr / ni = const
So can predict angle change! Polarization Non-polarized (usual)
light:
Each photon vibrates as a wave form in a single plane Light beam =
numerous photons, each vibrating in adifferent plane Vibration in
all directions ~ perpendicular to propagationdirection 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 ni varies with vibration direction. Vectors radiating
from center Length of each proportional to ni 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 ni the same (by definition) What is the
shape of an isotropic indicatrix? a spherical indicatrix The
Optical Indicatrix
North South A P P For isotropic minerals When analyzer inserted =
crossed-nicolsor XPL shorthand (vs PPL) no light passes extinct,
even when the stage is rotated Fig. 6-6 A Fig 6-6 Bloss, Optical
Crystallography, MSA West P P East Anisotropic crystals Calcite
experiment and double refraction Anisotropic crystals Calcite
experiment and double refraction
O E Double images: Ray 2 rays withdifferent propagationand
vibration directions Each is polarized ( ^ eachother) 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) 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 Fig 6-7 Bloss, Optical Crystallography, MSA Called
privileged directions Each ray has a different n w = no e =
nE
IMPORTANT:A given ray ofincoming light is restricted to only
2(mutually perpendicular) vibrationdirections once it enters
ananisotropic crystal Called privileged directions Each ray has a
different n w = no e = nE w < e(in the case of calcite) O E Fig
6-7 Bloss, Optical Crystallography, MSA 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
(caxis) ^ 2 identical ones--UNIAXIAL MINERALS The optical
properties reflect this as well: ellipsoid ofrotation 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 (no unique plane containing ray and c-axis) only one ray
(O-ray) with n = w(doesnt split to two rays) extinct with analyzer
in and stays that way as rotate stage 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 nfrom w (true e) Fig. 6-12 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 betweene and w) ellipsoid and
conventions:
(+) crystal = prolatee > w (-) crystal = oblate e < w (-)
crystal: w > e oblate (+) crystal: e > w prolate Fig 6-11
Bloss, Optical Crystallography, MSA Summary: Circular Section
Principal Sections
(^ optic axis: all w's) extinct Principal Sections (have w and true
e: max & min n's)largest birefringence! Random Sections(e' and
w) always have w!! Any cut through center of a uniaxial indicatrix
will have w as one semiaxis Fig. 6-12 Color chart Shows the
relationship between retardation, crystal thickness, and
interference color 550 mm red violet 800 mm green 1100 mm
red-violet again (note repeat ) 0-550 mm = 1st order mm = 2nd order
mm= 3rd order... Higher orders are more pastel Example: Quartz w =
1.544 e = 1.553 w e 1.544 1.553
Data from Deer et al Rock Forming Minerals John Wiley & Sons
Example: Quartz w = 1.544 e = 1.553 Sign?? (+) because e >
w
e - w = and is called the birefringence (d) = maximum interference
color What color is this?? 1) Follow line 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 90o) 360orotation 4
extinction positions exactly 90o apart Conoscopic Viewing A
condensing lens below the stage and a Bertrand lens above it
Arrangement essentially folds planes of Fig cone 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
FiguresVery useful for determining optical properties of xl Fig
7-13 Bloss, Optical Crystallography, MSA Uniaxial Figure Circles of
isochromes Note vibration directions:
w tangential e' radial & variable magnitude Blackcross
(isogyres) results from locus of extinction directions Center of
cross (melatope) represents optic axis Approx 30o 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. 7-14 Accessory Plates
Use a 1st-order red (gypsum) plate
Fig 8-1 Bloss, Optical Crystallography, MSA 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
thatD = (N-n) 550nm retardation thus it has the effect of retarding
the N ray550 nm behind the n ray If insert with no crystal on the
stage 1- order red in whole field of view Accessory Plates N
Suppose we view an anisotropic crystal with D = 100 nm (1-order
gray) at 45o from extinction n If Ngyp || Nxl Addition Addition
since ray in xl || Ngyp already behind by 100nm & it gets
further retarded by 550nm in the gypsum plate 650nm On your color
chart what will result? Original 1o grey 2o blue N Optic Sign
Determination
For all xls remember e' vibrates in plane of ray and OA, w vibr
normal to plane of ray and OA O E e ' w 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 (+)crystals: e > w so w faster Fig 7-13
Bloss, Optical Crystallography, MSA Optic Sign Determination
Inserting platefor 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 e ' w
sub add add sub (+)crystals: e > w so w faster N (+) OA Figure
with plate
(+) 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 = smallest n(fastest) b = intermediate n g =
largest n(slowest) The principal vibration directions are x, y, and
z( x || a, y || b,z || g) By definition a < a' < b < g
'< g Biaxial Crystals g If a < b < g then there must be
some point between a & g with n = b Because =b in plane, and
true b is normal to plane, then the section containing both is
acircular section 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 = b a Looking down true b Biaxial Crystals ^ optic
axis by definition g
If a < b < g then there must be some point between a & g
with n = b OA ^ optic axis by definition = b a Looking down true b
Biaxial Crystals ^ optic axis by definition
g If a < b < g then there must be some point between a &
g with n = b OA OA ^ optic axis by definition And there must be
two! Biaxial Hexagonal and tetragonal are Uniaxial = b a = b
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 ^ OAP= optic normal Fig 10-2 Bloss,
Optical Crystallography, MSA Acute angle between OA's = 2V The
axisthat bisects acute angle = acute bisectrix = Bxa The axisthat
bisects obtuse angle = obtuse bisectrix = Bxo Biaxial Crystals B(+)
defined as Z (g) = Bxa
Thus b closer to a than to g OA OA = b a = b Looking down true b
Biaxial Crystals B(-) defined as X (a) = Bxa
g B(-) defined as X (a) = Bxa Thus b closer to g than to a = b OA a
OA = b Looking down true b Biaxial Interference Figures
Fig Bloss, Optical Crystallography, MSA Bxa figure Result is this
pattern of isochromes for biaxial crystals Biaxial Interference
Figures
Centered Bxa Figure Fig Bloss, Optical Crystallography, MSA Biaxial
Interference Figures
Same figure rotated 45o Optic axes are now E-W Clearly isogyres
must swing Fig 10-16B Bloss, Optical Crystallography, MSA Centered
Optic Axis Figure Large 2V:
As rotate Centered Optic Axis Figure Large 2V: Bxa Figure with
Small 2V: Not much curvature Biaxial Optic Sign B(-) a = Bxa thus b
closer to g add subtract add
100 gray 650 blue Fig. 11-1A add subtract add 100 gray 450 yellow
Biaxial Optic Sign B(-) a = Bxa thus b closer to g (in stage)
add
subtract Centered Bxa 2V = 35o Centered Bxa 2V = 35o With accessory
plate Biaxial Optic Sign B(+) g = Bxa thus b closer to a (in stage)
sub add
Fig. 11-1A sub add sub Estimating 2V Fig 11-5A Bloss, Optical
Crystallography, MSA OAP
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