Review of Optical Mineralogy GEOL 5310 Advanced Igneous and Metamorphic Petrology 9/9/09

Nature of Light  Visible light is a form of electromagnetic radiation, which can be characterized as pulses or waves of electrical energy  Travels in straight lines with a transverse wave motion Unpolarized light Polarized light

Attributes of Light Wavelength (distance between wave peaks; measured in angstroms (Å); defines color of visible light Amplitude (A) height of light waves; corresponds to the intensity/brightness of light Frequency ()  number of light waves passing a fixed point per second; measured in cycles/second Velocity (v = ·); speed of light in a vacuum = 3·10 18 Å/sec = c e.g. for orange light in a vacuum, Å,  = 5·10 14 /sec Light slows down as it passes through denser substances. Because the frequency of light never changes as it passes through different substances, a decrease in light velocity reflects a proportional decrease in its wavelength.

Electromagnetic Spectrum From Bloss, 1961

Reflection and Refraction of Light  When light passes from a low density medium (e.g. air) into a higher density non-opaque medium (e.g. a mineral), part will be reflected and part will be pass through, but be bent and slowed – refracted.  Angle of reflection (  r’ ) equals the incident angle (  i )  Angle of refraction (  r ) will differ from the incident angle depending on the change in velocity between the two substances

Refractive Index and Snell’s Law Index of Refraction – n n substance = c / v substance >1 n substance = c / v substance >1 light velocity in air ≈ c, so n air ~ 1 Snell’s Law- predicts the angle of refraction at the interface of two substances with different refractive indicies: n i sin  i = n r sin  r  r = sin -1 (n i /n r x sin  i )

Successive Refraction

Refraction, Relief, and the Becke Line Relief is the degree to which a phase stands out from its surroundings and is an expression of the contrast in index of refraction dark outline

Becke Line Test From Bloss (1961)

Dispersion  Because n is related to light velocity, which is related to wavelength ((v = ·), different wavelengths of light will have different refraction indicies within a particular substance  Illuminating a mineral with white light may thus lead to color dispersion

Polarization of Light  Light emanating from a point source vibrates in all directions normal to the propagation direction  Light can be polarized (made to vibrate in one plane) by selective absorption (OR) or by reflectance (OL)

Anisotropy Indicies of refraction can vary in all minerals (except those in the isometric system) depending on the orientation of light ray. Such minerals are said to be anisotropic. Isometric minerals, glass, liquids and gasses have a single refraction index value regardless of the orientation of light rays. Such substances are said to be isotropic.

Optical 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 IsotropicIsometric Anisotropic – Uniaxial TetragonalHexagonal Anisotropic-BiaxialOrthorhombicMonoclinicTriclinic

Isotropic Indicatrix n A sphere whose radius corresponds to the characteristic refraction index- n n Diagram shows change in n for different wavelengths of light in same mineral 4861ÅBlue5893ÅYellow 6563Å Red n n=c/v =c/

Optical Recognition of Isotropic Minerals From Bloss (1961) Total Extinction under X-polars Slowing of ray = shortening of wavelength, but no change in polarity

Anistropic Minerals All randomly oriented anisotropic minerals cause double refraction (splitting) of light resulting in mutually perpendicular-polarized light rays. n One ray has a higher n (slow ray, or the ordinary ray) than the other ray (the fast ray, or extraordinary ray) Fast ray Slow ray

Birefringence (  ), Retardation(Δ), and Interference Colors nn Δ = d*  = n slow ray – n fast ray Δ = d* 

Uniaxial Indicatrix Optic Axis = C axis in tetragonal and hexagonal crystals

Sections 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 Section of the Uniaxial Indicatrix

Extinction of Uniaxial Minerals

Conoscopic Interference Figures of Uniaxial Minerals Orthoscopic Conoscopic Isochromes – zones of equal retardation equal retardation Isogyres – represent the areas where the ω and ε’ vibration directions are oriented N-S, E-W

Uniaxial Optic Axis (OA) Figure Circular section parallel to stage  = 0

Off-centered OA Figure Random section parallel to stage,  < 0, « max 

Very Off-centered OA Figure Random section parallel to stage,  « 0, < max 

Flash Figure Principal section parallel to stage,  = max 

Determining the Optic Sign of Uniaxial Minerals Connect the quadrants that go down in color (to yellow), compare with slow direction of gypsum plate for sign +

Biaxial Indicatrix Principal vibration axes n greatest n n lowest n n intermediate n < ’<<’<

Circular Sections and Optic Axes Circular Section OpticAxes OpticPlane

2V and the Optic Sign + - Trace of Circular Sections

Random Section through the Biaxial Indicatrix Vibration plane parallel to stage Double refraction rays

Variable Birefringence within a Biaxial Mineral =0 =max

Biaxial Optic Axis Figures Look for a mineral with the lowest interference colors, i.e. ~0

Acute Bisectrix Figures (Bxa) Melatope (emergence of optic axes)

Determining the Optic Sign of Biaxial Minerals D + D - U U D D D D ’ is fast ray  is intermediate ’ is slow ray - + X X U U U U

Estimating 2V by Curvature of Isogyre

Estimating 2V by Separation of Isogyres

Extinction Angle Symmetrical ParallelInclined

Sign of Elongation slowray Example – Length slow Interference colors increase Slowing down the slow ray