OPTICAL PROPERTIES OF MINERALS
 Nature of light (EM Radiation)
 To account for all properties of light we need wave theory and
corpuscular theory
 We use wave theory to explain the optical behavior of crystals
 Assume that visible light travels in straight lines with a
transverse motion (vibrates at right angles to direction of
propagation)
 Waves in light are like waves in water:
Wavelength =  (distance between successive crests)
Amplitude = displacement on either side of the equilibrium
 =frequency= #of waves /sec passing a point
v=velocity= frequency x wavelength
v=
 However, with light, transverse vibrations takes place  to the
direction of propagation in all possible directions
 R O Y G B I V
 7700Å
3900 Å
 White light = all wavelengths between 7700 and 3900 Å
 Single wavelength = monochromatic
C= speed of light = 3 x 108 m/sec
 When light passes through a mineral,  (wavelength) changes
but  (frequency) remains the same
INTERFERENCE
 Phase character of light (wave moving up or down at a
particular time ) in phase vs. out of phase
 2 waves in phase = Constructive interference
 increased intensity
 2 waves out of phase = Destructive interference
(if waves are of same , perfect C or D might occur)
POLARIZATION OF LIGHT AND THE POLARIZING MICROSCOPE
 Polarized light
vibration of light is  to direction of
propagation. With light, vibration is in all different directions
 We can filter or alter light to make all waves vibrate in one
direction || to a particular plane = plane polarized light
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HOW?
1) BY REFLECTION: light vibrates in planes || to the
reflecting surface, light traveling in other directions is
absorbed (polarizing sunglasses reduce glare)
2) BY ABSORPTION: all directions absorbed by an
anisotropic crystal. Two polarized rays are created one is
absorbed, one emerges
3) BY DOUBLE REFRACTION: light is bent by an anisotropic
crystal
2 polarized rays at different angles,
and we use one
We utilize filters. With one filter our eyes can’t tell if light is
polarized.
With a second filter we can!
If the 1st and 2nd filters are in || directions, then maximum light
is emitted / passes through.
If the 2nd filters are  to the 1st filter, then no light passes
Intermediate angles
intermediate amounts of light
POLARIZING MICROSCOPE (PETROGRAPHIC MICROSCOPE)
 Magnify with a white light source
 Lower polarizer – plane polarized light vibrating in only one
plane
 Typically in an E-W (Left-Right) direction
 Fixed condensing lens and diaphragm helps concentrate light
on the sample
ORTHOSCOPIC ILLUMINATION – UNFOCUSED BEAM
 Light travels from the substage through the sample and up the
microscope tube
 All light travels orthogonal ( to) stage
CONOSCOPIC lens + illumination = Condenser lens
Light converges on a small spot with a cone of nonparallel rays
 Rotate stage to change orientation of the sample relative to
polarized light
 Because most minerals are anisotropic (non-cubic) light
vibrates unequally in different directions, thus interaction with
light varies with stage rotation
OBJECTIVE LENSES (2x –50x typically)
N.A. (Numerical aperture) = describes angles at which light can
enter a lens (N.A. =.85 is most common)
OCULAR LENSES (8x,10x ,15x etc) in the eye piece
Total magnification = ocular x objective
(e.g. 10x X 20x = 200X)
Upper polarizer = Analyzer (insert or remove)
Typically at 90˚ to lower polarizer
 If no sample is on the stage and the upper polarizer is in, no
light can pass.
 If a sample is on the stage, it typically changes the polarization
of the light
 If isotropic – no light passes
 If anisotropic – some light passes
ACCESSORY PLATE
 Full wave plate (used to be gypsum plate)
 Bertrand lens + diaphragm (conoscopic study) (pin hole)
 Only polarizer = Plane Polarized Light (PPL)
 Both polarizers = Crossed Polar Light (CPL or XPL)
 PPL
grain size, shape, color, cleavage
 PPL
refractive index, pleochroism
 CPL
with conoscopic + Bertrand lens
retardation, optic sign, 2V
 Grain mounts + thin sections
Grains with refractive index oil and cover slip
T sections are 30m thick (thickness affects color)
 Colors in PPL + CPL
PPL in thin sections most minerals are weakly colored to
colorless
Changes in color under PPL with stage rotation are due to
changes in the minerals orientation with respect to polarized
light
= Pleochroism (useful for Identification of some minerals)
For uniaxial minerals = 2 hues
for biaxial minerals = 3 hues (XYZ Pleochroic formula)
light vibrates || to 3 directions that are numerically
perpendicular.
CPL INTERFERENCE COLORS
 Not caused by absorption of different wave lengths, but by
interference of light waves passing through the upper polarizer
 Differ based on grain orientation
 Vary with grain thickness
 Need T-Sections of uniform thickness
VELOCITY OF LIGHT IN CRYSTALS + REFRACTIVE INDEX
 When EMR passes near an atom, it causes electrons to
oscillate. This causes Energy to be absorbed from the light and
the wave slows down.
 A waves velocity through a crystal is described by the
Refractive index (n) of the crystal and it depends on chemical
composition, crystal structure and bond type
n = VVacuum /VCrystal
Because light in a vacuum is faster n is always > 1
( in air n = 1.00029  speed in vacuum, common reference)
n = Vair /VCrystal
 As light passes through most non opaque crystals its V decreases
by about 1/3 to ½ (n= 1.5 to 2 typically)
*
Because the frequency of light () is unchanged,  must
decrease because v= 
 Refractive index is most useful for grain mounts (with oils)
 R.I. also varies with  of the light used (need to eliminate this)
 Velocity of light in a crystal varies with light’s color (dispersion)
e.g. a prism separates white light into a rainbow
 Different ’s are bent (refracted) at different angles
Diamond = high dispersion
Fluorite = low dispersion
ISOTROPIC MINERALS (Cubic minerals, glass, epoxy + plastic)
 Have essentially random atomic structure
 Remain extinct (dark) as the stage rotates, no matter what their
orientation
ANISOTROPIC MINERALS
 Go extinct (briefly) every 90˚ of stage rotation (however if they
are oriented parallel to optic axis they will remain extinct and
appear isotropic)
 Anisotropic minerals may have only one (uniaxial) or two
(biaxial) optic axes. When in doubt if anisotropic or isometric,
use conoscopic light, as anisotropic minerals will transmit some
conoscopic light and display interference figures (isotropic
minerals do not)
SNELL’S LAW + LIGHT REFRACTION
 Objects appear to bend as they pass from air into water =
refraction, as light passes from one medium into another, with
different R.I.’s

If light strikes the interface at an angle ≠ 90˚,it changes
direction
 the light beam bends towards the medium with the higher R.I.
because one side of the beam moves faster than the other.
 The angle between the incoming beam and a perpendicular to
the interface is i the angle of incidence
 The angle between the outgoing beam and a perpendicular to
the interface is the angle of refraction=r
 The relation between the two angles is
Sin i / Sin r = Vi/Vr = nr/ni
where Vi and Vr are velocities of light through the two media
ni and nr are the indices of refraction of the two media
= Snell’s law (Dutch 1621)
by rearranging, we calculate the angle of refraction:
r = sin-1 [ ni/nr Sin i ]
by definition, Sin values of i must be  1.0
for some/average values of i there is no solution.
The limiting value of i is the critical angle of refraction.
 If the angle is greater no light escapes and the entire beam is
reflected inside the crystal= high R.I. of diamond and
adamantine luster (sparkling appearance).
 We can use a refractrometer to measure the angle.
RELIEF AND BECKE LINES
 Isotropic minerals in liquid of the same R.I. disappear (unless
they are distinctly colored) as their edges don’t stand out.
 If the grains have a significantly different R.I. than the liquids
light will refract and reflect at the edge of the grain and the
boundary becomes more pronounced.
RELIEF
 Contrast between a mineral and its surroundings (high vs. low)
 Also true in T-sections relative to epoxy or other minerals
If a grain is in a liquid, some light rays bend towards the medium
with higher R.I.
Light interacts with the grains as if they were small lenses. If
Nmineral >nliquid, rays are refracted and converge after passing
through the grain.
We can see this feature if we slowly lower the microscope stage,
shifting the focus to a point above the mineral grain.
A bright narrow band of light called a BECKE LINE appears at the
mineral-liquid interface and moves towards the material with the
higher R.I.
( A complimentary but harder to see, dark band moves towards the
material with the lower R.I.)
 We can do the same thing in a T-Section by focusing and
at a grain boundary.
 We can employ a variety of oils of differing R.I. to identify the
R.I. of an unknown mineral grain.
INTERACTION OF LIGHT AND CRYSTALS
DOUBLE REFRACTION
Upon entering an anisotropic mineral, light is normally split into two
polarized rays, each traveling through the crystal along a slightly
different path with a slightly different velocity and R.I.
For uniaxial minerals we call the two rays:
O (ordinary) ray  and
E (extraordinary) ray ’
The O ray travels a path predicted by Snell’s law, while the E ray
does not. The O ray and the E ray vibration directions depend on
the direction that light is traveling through the crystal structure, but
the vibration direction of the two rays are always perpendicular to
each other.
 We call the splitting of a light beam into 2 perpendicularly
polarized rays, double refraction. All randomly oriented
anisotropic minerals cause double refraction.
 Calcite is one of the few common minerals that exhibit double
refraction that is easily seen without a microscope.
 As the two rays pass through an anisotropic crystal, they travel
at different velocities (unless they are parallel to an optic axis)
 We call the two rays the slow ray and the fast ray.
 Because they travel at different velocities, their R.I’s must be
different
 The difference in the indices of the fast and slow rays (nslow- nfast)
is the apparent birefringence (’)
 The maximum birefringence () is a diagnostic property of
minerals.
 When the slow ray emerges from the anisotropic crystal, the fast
ray has already emerged and traveled some distance. This
distance is the retardation (). Retardation is proportional to
both the thickness (t) of the crystal and to the birefringence in
the direction the light is traveling (’).
=t x (’)=t x (ns-nf)
For isotropic crystals,  and  = 0
All light passes through them with the same velocity
(see table inside back cover of the book for interference colors,
which are a function of birefringence)
CRYSTALS BETWEEN CROSSED POLARS
Under CPL we can differentiate isotropic and anisitropic crystals
(isotropic remains dark through 360 of stage rotation)
When we view an anisotropic crystal with CPL (unless down an
optic axis) light is split into 2 rays. The 2 rays, after emerging from
the crystal, travel up to the upper polariser where they are resolved
into one ray with N-S polarization. Because the vibration directions
of the rays are not normally perpendicular to the upper polarizer,
components of both pass through it to produce the light reaching
our eyes.
As we rotate the microscopic stage, the relative intensity of the two
rays vary. Every 90 the intensity of one is zero and the other is
vibrating parallel to the lower polarizer.
Consequently, no light passes through the upper polarizer and the
crystal appears extinct every 90 (at 45 to the extinction positions,
we see maximum brightness)
INTERFERENCE COLORS
When white light passes through an anisotropic mineral, all
wavelengths are split into 2 polarized rays vibrating at 90 to each
other.
 Different colors have different , so some colors may be retarded
(though most will not)
 When the N-S component of the two rays are combined at the
upper polarizer C.I. occurs for some colors and D.I. for others
 If we see a mineral of uniform thickness under CPL, we see one
color the interference color.
 Depends on retardation, which depends on orientation,
birefringence and the thickness of the crystal.
 Interference colors change intensity and hue as we rotate the
stages they disappear every 90
 Normal interference colors are shown in a Michel – Levy color
chart
 Very low order interference colors (retardation of < 200nm) are
gray + white
 The interference color of a mineral with very low birefringence
changes from white to black every 90
 Minerals with slightly greater birefringence show yellow, orange
or red interference colors upon rotation (retardation of 200-550
nm) = first order colors
 As retardation increases further, colors repeat every 550nm
(average wavelength of visible light) going from violet to red
(second order) and then from violet to red again (3rd order)
 They become more pastel as order increases.
 4th order colors appear white
 Calcite (=.172) with high order pastels and quartz (=.011)
with 1st order gray-white.
 If in doubt insert a full wave plate
 ’s 1st order white to yellow or blue, but has no effect on high
order white
 some minerals have anomalous interference colors (due to high
dispersion or if they are deeply colored): chlorite, epidote,
zoisite, jadeite, tourmaline, sodic plagioclase
UNIAXIAL & BIAXIAL MINERALS
 Isotropic crystals have the same R.I. in all directions because
they have the same light velocity in all directions.
 Anisotropic minerals do not
For uniaxial minerals we need 2 indices of refraction to describe the
mineral R.I. ( and  ). For biaxial minerals we need three (, 
and )
Optic axes are directions that light can travel through a crystal
without being split into 2 rays
 In some uniaxial minerals, the O.A. is parallel or perpendicular to
crystal faces
 In biaxial minerals, the 2 optic axis rarely are parallel or
perpendicular to crystal faces
Light traveling parallel to O.A. of a uniaxial mineral travels as an
ordinary ray with a unique R.I. 
Light traveling in other directions is doubly refracted
rays:  and ’ R.I.’s
’ is a value between  and  (light perpendicular to O.A.)
2
 If < = uniaxial (+)
 If > = uniaxial (-)
 POLE (positive = omega less than epsilon)
 NOME (negative = omega more than epsilon)
Maximum possible bifringence, , =|-| (if O.A. is parallel to stage)
Most minerals are biaxial. We describe their optical properties in
terms of 3 perpendicular directions (x, y, z)
Fig. 7.23
 The vibration direction of the fastest ray is X; the slowest is z
 The R.I. for light vibrating parallel to x, y and z are ,  and 
 Thus  has the lowest R.I.,  the highest, and  intermediate.
(R.I. of light perpendicular to an O.A.)
 Normally light that passes through a randomly oriented biaxial
crystals is split into two rays, neither of which vibrates parallel to
x, y, and z.
 Thus their R.I.’s will be some value between  and 
 If light travels parallel to y, the rays will have R.I’s equal to 
and  as they vibrate parallel to x and z
 In this case the crystal will experience maximum retardation
 If light travels parallel to an optic axis, no double refraction
occurs and it has a single R.I. 
 There will be no birefringerence or retardation and the mineral
will appear extinct
In biaxial minerals we call the plane that contains x and z, and the 2
optic axis the optic plane
 The acute angle between the optic axis is 2V
 A line bisecting the acute angle must parallel either z (biaxial +)
or X (biaxial -)
 In biaxial (+) minerals  is closer in value to  than to 
 In biaxial (-) minerals,  is closer in value to 
 The maximum possible value of birefengerence in biaxial
minerals () is always  - 
Accessory plates and sign of elongation
 When inserted above the objective lens, the slow and fast
vibration directions of the plate are at 45 to the upper and lower
polarizers.
 A full wave plate has a retardation of 550 nm (avg wavelength of
light)= first order red interference colors
 Quartz wedge has variable thickness with retardation from 0 to
3500 nm
 Inserting a plate adds or subtracts to the retardation.
 We can determine which direction in the crystal permits polarized
light to travel the fastest
 If crystals have a long dimension we can determine if the mineral
is length fast (negative elongation) or length slow (positive
elongation)
UNIAXIAL INTERFERENCE FIGURES
 Optic sign (+ or -) is another useful characteristic to identify
anisotropic crystals.
 Interference figure use conoscopic light with upper polarizer in
and a Bertrand lens (refocuses rays + magnifies I.F)
 To determine the optic sign of a uniaxial mineral it is best to look
down the optic axis=optic axis figure =O.A. = uniaxial cross
 Should be easy to find because uniaxial minerals appear isotropic
when we look down the O.A. or have low order interference
colors if we are close to O.A.
Melatope = center of cross where O.A. emerge
Isogyre = dark bands forming cross
Isochromes colored rings (if present) (bands of equal
retardation caused by light entering at different angles)
 Minerals with low birefringence (e.g. quartz) may not display
isochromes
To determine (+) or (-) sign we use an accessory plate
 Usually O.A. is not perfectly centered
 If O.A. is parallel to the stage of the microscope we get an optic
normal figure = flash figure
 Appears as a vague cross or blob that nearly fills the field of view
when the grain is at extinction (= when the O.A. is perpendicular
to one of the polarizers)
 Upon stage rotation it splits into 2 curved isogyres flashing in
and out of the field of view with a few degrees of stage rotation
 Looks like a BXO figure
BIAXIAL INTERFERENCE FIGURES
 It is more difficult to find grains oriented in a useful way for
biaxial crystals.
3 general types of biaxial interference figures: optic axis; acute
bisectrix (Z axis); and optic normal (Y axis)
ACUTE BISECTRIX FIGURE (BXA)
Z axis is perpendicular to the polarizer or analyzer (you are
looking down optic plane (X-Z)
 Black cross is similar to uniaxial I.F.
 Upon rotation cross splits into 2 isogyres that move apart and
may leave the field of view
 After 45 rotation isogyres are at max separation, another 45
resume +
 the maximum amount of isogyre separation 2V depends on RI
and K (constant based on numeric aperture of objective lens)
 if 2 V is , 60 , iosgyres stay in the field of view on rotation
BXA figures for topaz [2v=60] and muscovite [2v =40]
 The points on the isogyres closest to the center of a BXA (or
BXO), the melatopes are points corresponding to the orientations
of the optic axes
 If the crystal retardation is great, isochromes circle the
melatopes
 Interference colors increase in order, moving away from the
melatopes because retardation is greater as the angle to the
optic axis increases
Optic Axis Figure – Maximum curvature of isogyre can also be used to
estimate 2V angle
OBTUSE BISECTRIC FIGURE
(BXO)
 The isogyres in a BXO figure always leave the field of view on
rotation because, by definition, an obtuse angle separates the
optic axis in the BXO direction
 If isogyres remain on rotation=BXA
 If not = either a BXA with 2V >60 or BXO
 Perfectly centered BXO or BXA are rare. It may be possible to
see only one isogyre clearly
DETERMINIG OPTIC SIGN FROM A BXA
= does the BXA correspond to fast direction (-) or slow direction
(+)?
 Need a useful for BXA when isogyres remain in field of view
Or
Find a grain with a centered optic axis figure (OA)
 Amount of curvature =2V
 More curvature = lower 2V
DETERMINIG OPTIC SIGN FROM A BXO
OPTIC NORMAL FIGURE
 Looking down Y axis, perpendicular to plane with 2 optic axis
 Grain with maximum retardation poorly resolved BXA, but
isogyres leave the field of view with only slight rotation.
 Appear similar to the uniaxial flash figures.
EXTINCTION ANGLES
– Uniaxial Minerals
- Biaxial Minerals
Uniaxial - Sign of Elongation