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EARTH
MATERIALS
OPTICS AND
MINERALS
Wave Terms
FREQUENCY (f) number of cycles per unit time
[units = Hertz (Hz)]
1 Hz = 1 cycle/s
T = 1/f; f = 1/T; T f = 1
Waves can coexist in the same space with other waves.
Waves interact in various ways.
Waves that are in phase experience constructive
interference.
Image by E.B. Watson
waves that are out of phase experience
destructive interference...
Image by E.B. Watson
Objects radiate light because of their high
temperatures - incandescent.
light (EM) is produced whenever a charge is
accelerated by an external force...
Image by E.B. Watson
electromagnetic wave model
Visible light – part of the EM spectrum
Image by E.B. Watson
Longer l
v = lf, and v = c
Peak solar
Image by E.B. Watson
Waves may be
•Absorbed
•Transmitted
Refracted
•Reflected
Image by E.B. Watson
Index of refraction (n) for EM
Refraction
c
n
v
Image by E.B. Watson
air (0oC)
air (30oC)
Glass
Diamond
Ice
Water
Alcohol
1.00029
1.00026
1.50
2.42
1.31
1.33
1.36
“You know how a stick looks bent when you put it in
water? That’s why I no longer take baths.”
Steven Wright
Image by E.B. Watson
Image by E.B. Watson
Snell’s law
sin i v B na


sin r v A nb
Critical Angle
Image by E.B. Watson
All you need to find this is to
solve Snell’s law for r =90O
Polarization
Image by E.B. Watson
Plane Polarization
Filter
Image by E.B. Watson
When monochromatic light is transmitted
through a mineral from air, its velocity slows,
the waves bunch up. The frequency remains
the same but the wavelength decreases.
Refraction – producing constituent
wavelengths
Image by E.B. Watson
Dispersion
High f (low l) – more bending in prism
The index of
refraction decreases
with increasing
wavelength. The nD is
at 589 nm.
Abnormal dispersion
of the ri (increased at
higher l). Minerals
with abnormal
dispersion are always
colored.
Immersion oils of fixed ri can
identify the ri of an unknown
grain.
If the mineral has a higher ri =
positive relief
If the oil has a higher ri =
negative relief
Lowering the stage of a
microscope, the focus
(Becke) line moves to the
material with higher ri.
Isotropic
Same in every
direction. Light is
refracted equally in all
directions in these
materials.
Isometric forms
(cubic)
Non-lattice structures
Glasses, polymers,
liquids, gasses.
ri is uniform
Uniaxial
Two principle
directions at right
angles.
Tetragonal
Hexagonal
Rhomobohedral
2 configurations
If c > a then (+)
If c < a then (-)
Two ri
Uniaxial
•Those with atoms equally spaced along two axes,
elongated in the third.
•Requires two raypaths, one in the close packed
plane, one perpendicular.
The ordinary () ray and the extraordinary () ray
•If the extraordinary ray is the slow ray, then the
mineral is optically positive
•If the extraordinary ray is the fast ray, then the
mineral is optically negative.
Anisotropy results when
atoms are closely packed
in one plane, and further
apart in another.
In anisotropic materials,
the velocity of light varies
depending on direction
through the material
In most directions, light
that enters splits into two
rays that vibrate and right
angles to each other.
d = thickness
D = retardation
Interference at the analyzer
The retardation is a
full wavelength - the
fast and slow rays
constructively
interfere perpendicular
to the analyzer
The retardation is a
half wavelength - the
fast and slow rays
constructively
interfere in the pole of
the analyzer
Michel-Levy Interference Color Chart
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Nikon Microscopes
Color
Interference (birefringence)
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Uniaxial
Uniaxial
Interference figures
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Fast on slow -colors go low
Biaxial crystals
Three principle
directions, not
necessarily at right
angles.
Orthorhombic
Monoclinic
Triclinic
Biaxial crystals
•Those with atoms unequally spaced along the three
crystallographic axes.
•Requires three raypaths for each direction
The a, b, g rays
a is lowest ri, fastest
g is highest ri, slowest
b is the middle child
•This produces two optical axes, separated by an
acute angle 2Va.
•If 2Va is bisected by ng, then positive.
•If 2Va is bisected by na, then negative
Biaxial
http://www.brocku.ca/earthsciences/people/gfinn/optical/bxsign1.htm
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http://edafologia.ugr.es/optmine/xplconos/fbtallaw.htm
Minerals retard light relative to air
Light is refracted as a function of the velocity
difference.
Polarization eliminates all but one vibration
direction
Isotropic materials have only one velocity - no
interference
Uniaxial minerals have two raypath velocities optic axis is on c and exhibit interference
Biaxial minerals have three raypath velocities - two
optic axes and exhibit interference