Review of Optical MineralogyReview of Optical Mineralogy

GEOL 5310GEOL 5310Advanced Igneous and Metamorphic Advanced Igneous and Metamorphic

PetrologyPetrology

9/9/099/9/09

Nature of LightNature of Light

Visible light is a form of Visible light is a form of electromagnetic electromagnetic radiationradiation, which can be characterized as , which can be characterized as pulses or waves of electrical energypulses or waves of electrical energy

Travels in straight lines with a transverse Travels in straight lines with a transverse wave motionwave motion

Unpolarized lightPolarized light

Attributes of LightAttributes of LightWavelength (Wavelength (distance between wave peaks; measured in distance between wave peaks; measured in

angstroms (Å); defines color of visible lightangstroms (Å); defines color of visible light

AmplitudeAmplitude ((AA) ) height of light waves; corresponds to the height of light waves; corresponds to the intensity/brightness of lightintensity/brightness of light

Frequency (Frequency () ) number of light waves passing a fixed point per second; number of light waves passing a fixed point per second; measured in cycles/secondmeasured in cycles/second

Velocity (Velocity (vv = = ··)); speed of light ; speed of light in a vacuum in a vacuum = = 3·103·101818 Å/sec = Å/sec = cc

e.g. for orange light in a vacuum, e.g. for orange light in a vacuum, Å, Å, = 5·10 = 5·1014 14 /sec/sec

Light slows down as it passes through denser substances. Because Light slows down as it passes through denser substances. Because the frequency of light never changes as it passes through different the frequency of light never changes as it passes through different substances, a decrease in light velocity reflects a proportional substances, a decrease in light velocity reflects a proportional decrease in its wavelength.decrease in its wavelength.

Electromagnetic SpectrumElectromagnetic Spectrum

From Bloss, 1961

Reflection and Refraction of LightReflection and Refraction of Light

When light passes from a low density medium (e.g. air) When light passes from a low density medium (e.g. air) into a higher density non-opaque medium (e.g. a mineral), into a higher density non-opaque medium (e.g. a mineral), part will be part will be reflectedreflected and part will be pass through, but be and part will be pass through, but be bentbent and slowedand slowed – – refracted.refracted.

Angle of Angle of reflectionreflection ( (r’r’) equals the incident angle () equals the incident angle (ii))

Angle of Angle of refractionrefraction ( (rr) will differ from the incident angle ) will differ from the incident angle

depending on the change in velocity between the two depending on the change in velocity between the two substancessubstances

Refractive Index and Snell’s LawRefractive Index and Snell’s Law

Index of Refraction –Index of Refraction – n n

nnsubstancesubstance = c / v = c / vsubstancesubstance >1 >1

light velocity in air ≈ light velocity in air ≈ cc, so , so nnairair ~ 1 ~ 1

Snell’s Law-Snell’s Law- predicts the angle of refraction predicts the angle of refraction at the interface of two substances with at the interface of two substances with different refractive indicies:different refractive indicies:

nnii sin sin i i = n= nrr sin sin r r

r r = sin= sin-1-1 (n (nii/n/nrr xx sin sin ii))

Successive RefractionSuccessive Refraction

Refraction, Relief, and the Becke Refraction, Relief, and the Becke LineLine

ReliefRelief is the degree to which a phase stands is the degree to which a phase stands out from its surroundings and is an out from its surroundings and is an expression of the contrast in index of expression of the contrast in index of refraction refraction

dark outline

Becke Line Test Becke Line Test

From Bloss (1961)

DispersionDispersion Because Because nn is related to light velocity, which is is related to light velocity, which is

related to wavelength (related to wavelength (((vv = = ··)), different , different wavelengths of light will have different refraction wavelengths of light will have different refraction indicies within a particular substance indicies within a particular substance

Illuminating a mineral with white light may thus lead Illuminating a mineral with white light may thus lead to color dispersionto color dispersion

Polarization of LightPolarization of Light

Light emanating from a Light emanating from a point source vibrates in point source vibrates in all directions normal to all directions normal to the propagation the propagation directiondirection

Light can be polarized Light can be polarized (made to vibrate in one (made to vibrate in one plane) by selective plane) by selective absorption (OR) or by absorption (OR) or by reflectance (OL)reflectance (OL)

AnisotropyAnisotropy

Indicies of refraction can vary in all minerals Indicies of refraction can vary in all minerals (except those in the isometric system) (except those in the isometric system) depending on the orientation of light ray. depending on the orientation of light ray. Such minerals are said to be Such minerals are said to be anisotropicanisotropic. .

Isometric minerals, glass, liquids and gasses Isometric minerals, glass, liquids and gasses have a single refraction index value have a single refraction index value regardless of the orientation of light rays. regardless of the orientation of light rays. Such substances are said to be Such substances are said to be isotropicisotropic. .

Optical IndicatricesOptical Indicatrices• A 3-d map of the indices of refraction for various vibration directions of light rays• Orientation of the indicatrix within a mineral is symmetrical with the

crystallographic axis

IsotropicIsotropic

IsometricIsometric

Anisotropic – UniaxialAnisotropic – Uniaxial

TetragonalTetragonalHexagonalHexagonal

Anisotropic-Anisotropic-BiaxialBiaxial

OrthorhombicOrthorhombicMonoclinicMonoclinic

TriclinicTriclinic

Isotropic IndicatrixIsotropic Indicatrix

A sphere whose radius corresponds to the characteristic refraction index- nn

Diagram shows change in nn for different wavelengths of light in same mineral

4861ÅBlue4861ÅBlue5893ÅYellow5893ÅYellow6563Å Red6563Å Red

nn=c/v =c/

Optical Recognition of Isotropic MineralsOptical Recognition of Isotropic Minerals

From Bloss (1961)

Total Extinction under X-polars

Slowing of ray = shortening of wavelength, but no change in polarity

Anistropic Anistropic MineralsMinerals

All randomly oriented anisotropic minerals cause double refraction (splitting) of light resulting in mutually perpendicular-polarized light rays.

One ray has a higher nn (slow ray, or the ordinary ray) than the other ray (the fast ray, or extraordinary ray)

Fast rayFast raySlow raySlow ray

Birefringence (Birefringence (), Retardation(), Retardation(ΔΔ)), and , and Interference ColorsInterference Colors

= nnslow ray – nnfast ray ΔΔ = d* = d*

Uniaxial IndicatrixUniaxial IndicatrixOptic AxisOptic Axis

= C axis in tetragonal and hexagonal crystals

Sections of Uniaxial IndicatricesSections of Uniaxial Indicatrices = ω-ω = 0 (circular section)

= ε’- ω (random section)

= ε - ω (principal section)maximum birefringence

Total extinction in x-polar light

Re-Polarization of Light through a Non-circular Re-Polarization of Light through a Non-circular Section of the Uniaxial IndicatrixSection of the Uniaxial Indicatrix

Extinction of Uniaxial MineralsExtinction of Uniaxial Minerals

Conoscopic Conoscopic Interference Interference

Figures of Uniaxial Figures of Uniaxial MineralsMinerals

Orthoscopic Conoscopic

Isochromes – zones of Isochromes – zones of equal retardationequal retardation

Isogyres – represent the Isogyres – represent the areas where the areas where the ωω and and εε’ ’ vibration directions are vibration directions are oriented N-S, E-Woriented N-S, E-W

Uniaxial Uniaxial Optic Axis Optic Axis

(OA) (OA) FigureFigure

Circular section parallel to stage

= 0

Off-centered OA FigureOff-centered OA FigureRandom section parallel to stage, < 0, « max

Very Off-centered OA FigureVery Off-centered OA Figure

Random section parallel to stage, « 0, < max

Flash FigureFlash FigurePrincipal section parallel to stage, = max

Determining the Optic Sign of Determining the Optic Sign of Uniaxial MineralsUniaxial Minerals

Connect the quadrants Connect the quadrants that go down in color that go down in color (to yellow), compare (to yellow), compare with slow direction of with slow direction of gypsum plate for signgypsum plate for sign

+

Biaxial IndicatrixBiaxial IndicatrixPrincipal vibration axes

greatest nn

lowest nn

intermediate nn

< < ’<’<<<’<’<

Circular Sections and Optic AxesCircular Sections and Optic AxesCircular Circular SectionSection

Circular Circular SectionSection

Optic Optic AxesAxes

Optic Optic PlanePlane

2V and the Optic Sign2V and the Optic Sign

+ -

Trace of CircularSections

Random Section through the Random Section through the Biaxial IndicatrixBiaxial Indicatrix

Vibration plane parallel to stage

Double refractionrays

Variable Variable Birefringence Birefringence

within a within a Biaxial Biaxial MineralMineral

=0

=max

Biaxial Optic Axis FiguresBiaxial Optic Axis Figures

Look for a mineral with the Look for a mineral with the lowest interference colors, i.e. lowest interference colors, i.e. ~0~0

Acute Bisectrix Figures (Bxa)Acute Bisectrix Figures (Bxa)

Melatope (emergence Melatope (emergence of optic axes)of optic axes)

Determining the Optic Sign of Biaxial MineralsDetermining the Optic Sign of Biaxial Minerals

DD

++

DD

--

UU

UU

DD

DD

DD

DD

’ ’ is fast rayis fast ray

is intermediateis intermediate

’ ’ is slow rayis slow ray

--

++

X

X

UU

UU

UU

UU

Estimating 2V by Curvature of Estimating 2V by Curvature of IsogyreIsogyre

Estimating 2V by Separation of Estimating 2V by Separation of IsogyresIsogyres

Extinction AngleExtinction Angle

SymmetricalSymmetrical ParallelParallel InclinedInclined

Sign of ElongationSign of Elongation

slowslowrayray

Example – Length slowExample – Length slowInterference Interference colors increasecolors increase

Slowing down Slowing down the slow ray the slow ray