Interference figures Very important tool to determine optical characteristics. They will tell you: Uniaxial vs biaxial Optic sign 2V angle – for biaxial Used for estimating chemistry of mineral

Technique Focus with highest power objective Be certain observation is conoscopic light Flip in conoscope on some microscopes Most of them have to raise light sources as high as possible Insert Betrand lens or remove ocular Interference figure forms on top of objective lens Betrand lens required to refocus the image

Slightly more modern version Bertrand lens conoscope

One type of Uniaxial Interference Figure Isogyres Isochromes Melatope Fig. 7-35

Figure consist of isogyres and isochromes Isochromes: patterns of interference colors Isogyres: dark bands (extinction) Nature of interference figure and patterns as stage rotated determines optical property Types of figures controlled by cut of the grain

Uniaxial Interference Figure Three types: Optic axis figure Off-center optic axis figure Flash Figure Note – these correspond with the principle cuts of the indicatrix

Optic Axis Figure Forms when optic axis perpendicular to stage Grain exhibits low interference color (extinct)

Figure Black cross of isogyres Circular isochromes Melatope - location of optic axis Isochromes are increasingly higher order colors outward

Isochromes (and isogyres) result from ray paths of conoscopic light: Light traveling along optic axis (melatope) has no retardation Light near melatope has low retardation (d and d little higher Light far from melatope have higher retardation (d and d increase more) Thicker and high birefringent minerals have more isochromes E.g. calcite (large d) vs quartz (small d)

Thin section Indicatrix Longer path length, greater d, higher interference colors Perpendicular to light ray is section of indicatrix, larger d Fig. 7-36

Origin of Isochromes and Isogyres w rays vibrate tangent to isochromes e rays vibrate perpendicular to isochromes Isogyres are where vibration directions are N-S and E-W, extinct

Thin section Indicatrix Fig. 7-37 Note: each ray path has its own section of indicatrix; Each has unique ne’, so has increasing d outward Thin section Indicatrix Fig. 7-37

Off-center OA figure Figure forms when OA is not perpendicular to stage Correct grain will have intermediate interference colors Use of figure similar to centered OA figure

Off-center OA figure If OA < ~30º to stage, melatope in field of view Isogyres swing around center of cross hairs If melatope is out of field of view, difficult but possible to determine optic sign

Off-center OA, melatope in field of view Optic Axis inside field of view Fig. 7-38

Off-center OA figure, melatope outside field of view Thin section Indicatrix Optic Axis outside field of view Fig. 7-38

Optic Normal (Flash Figure) Formed when OA is parallel to stage Grains have highest interference colors Broad diffuse isogyres, split and leave field of view Not much use Determines orientation of OA – e.g. pleochroism

Fig.7-39

Determining Optic Sign Orientation of vibration directions known in each quadrant Insertion of accessory plate will cause subtraction and addition Determines sign

e>w - e<w + e’ always points toward melatope, Orientation of vibration directions from fig. 3-37 Addition Subtraction e>w - e<w + Fig. 7-40

Biaxial Interference Figures 5 major figures 2 useful ones: Acute bisectrix (Bxa) figure Optic axis figure 3 worthless ones: Obtuse Bisectrix (Bxo) figure Optic Normal figure (Flash figure) Off-center figure

Acute bisectrix figure Bxa axis (X or Z depending on sign) oriented perpendicular to stage Biaxial Indicatrix Fig. 7-27 Optically positive Optically negative

Acute bisectrix figure Grains have intermediate to low interference colors (depends on 2V) Isogyres form cross that splits and leaves field of view as stage is rotated Two melatopes (i.e. two OA) Isochromes are oval or figure 8 around the melatope

Acute bisectrix figure Optic Plane Optic Plane Grain 45º from extinction Grain at extinction Fig. 7-41

Optic Axis Figure Formed when OA is vertical These grains have zero or small retardation If 2V > 30º, only one melatope (OA) in field of view If 2V very small, looks like an off-center Bxa figure

2V < 30º 2V > 30º Fig. 7-44

Determining Optic Sign Done with Bxa or OA figure Example of Bxa figure: Two light rays vibrate along Bxa axis (either Z or X, the other must be Y) Y vibration is nb, this one is perpendicular to the optic plane Other depends if mineral is + or – If +, then vibration is X = na If -, then vibration is Z = ng Use accessory plate to determine if vibration is fast or slow

Two vibration directions depend on which axis is Bxa Addition Subtraction Fast on slow? Slow on slow? Shows if Bxa is Z or X Remember: Think about slice of indicatrix to give you vibration directions Two vibration directions depend on which axis is Bxa Fig. 7-48 Light from bottom

Determining optic sign with Biaxial OA figure Subtraction Addition Slow over fast - subtraction Slow over slow - addition Fig. 7-49

Determining 2V – several techniques Bxa figure: Spacing between melatopes relates to 2V Depends on numerical aperture (NA) of objectives Can guess within about 10º

Numerical aperture 15º 30º 45º 60º Fig. 7-51

Optic axis figure Curvature of the isogyre depends on 2V If 2V = 90º, the isogyre is a straight line If 2V = 0º, the isogyre forms a cross – it is uniaxial

Fig. 7-52