Todays objectives

1
Todays objectives

• What happens when light passes through most
  minerals?
• Why do some minerals change color when the
  microscope stage is rotated (without analyzer)?
• What causes the colors you saw when you inserted
  the analyzer?
• Why do those colors go to black every 90 degrees
  of rotation?
• How can we use those colors to help us identify
  unknown minerals?

2
Background

• Vectors
• Light as wave
• Interference (2D)
• Interference (3D)

3
Polarization

• Light can be constrained to vibrate in a
  particular plane
• When two light rays combine, their vibration
  vectors add (vector-wise)

ABC
4
Polarization

• Polaroid film (in the polarizer analyzer on
  your scope) absorbs light vibrating perpendicular
  to its direction

transmitted component
polarizer direction
incoming ray
5
Anisotropic materials

• Cause light to split into 2 rays vibrating 90 to
  each other
• Two rays see a different crystal environment
• different indices of refraction
• different speeds of light
• different paths
• produces double refraction

6
Double refraction

• Calcite demo
• One ray takes unexpected path through crystal
  (extraordinary, e or E ray)
• Special direction where this doesnt happen
  optic axis
• calcite nw 1.658 and ne 1.486
• which image looks deeper?

7
Double refraction
8
Pleochroism

• Two rays are absorbed differently
• can show different color (distribution of
  wavelengths)
• or intensity of color

9
Pleochroism

• Isometric - no pleo.
• Hexagonal, tetragonal - 2 end-member colors
• Triclinic, Monoclinic, Orthorhombic - 3
  end-members

10
Pleochroism

• Isometric - no pleo.
• Hexagonal, tetragonal - 2 end-member colors
• Triclinic, Monoclinic, Orthorhombic - 3
  end-members

11
Recap - Pleochroism

• Anisotropic grain has fast and slow directions
• In some minerals, these show different colors
• Because the incoming light is polarized, when one
  ray is perpendicular to that direction, it is
  excluded and the other color is displayed

12
Retardation

• fast slow rays are 45 from polarizer
• D d (ns - nf)
• distance, nm

d
13
Interference

• Retarded rays get vector-combined in analyzer
  (XP)

14
Interference

• If Dnl, no ray passes analyzer

15
Recap Retardation / Interference

• The slow ray is held back, so at the analyzer
  they combine with a new net vibration direction
  (retardation changes vibration direction)
• The relationship between the retardation
  distance, grain thickness, and indices of
  refraction is
• D d (ns - nf)
• If the new vibration direction is 0 or 180 from
  the incoming, the ray is canceled at the analyzer
  (upper polar)
• when Dl, or D2l , or D3l , or D4l , etc.

16
Extinction

• When fast or slow direction polarizer
• will occur every 90 of stage rotation
• Calcite demo

17
Interference Colors

• What changes for other colors (wavelengths)?
• D d (ns - nf)

d
18
Interference Colors

• Story above was for one wavelength (color) of
  light
• Retardation distance (D) is same across colors,
  but
• D n l -gt no ray (rotation 0 or 180)
• D n l - (l/2) -gt max.ray (rot.90, 270)
• Certain wavelengths get blocked at analyzer,
  others pass
• produces an interference color

19
Thickness effect

• D d (ns - nf)
• quartz wedge demo
• d (ns - nf) 0.009 (a small value)
• shows change in set of transmitted wavelengths
  (i.e., color) with increasing retardation, D

20
Birefringence effect

• D d (ns - nf) d d
• can get same set of colors by varying d at
  constant d
• maximum d is characteristic of mineral!
• e.g., calcite d 0.172 (a large value)
• orientation-dependent
• d (ns-nf) ranges from 0 to a maximum
• 0 is looking down optic axis

21
Interference Color Chart

• range of colors - same as quartz wedge
• measuring birefringence

birefringence, d
quartz?
thickness, d (µm)
birefringence, d
retardation, D (nm)
22
Interference Color Chart

• Orders
• Every 550 nm ( lblue)

birefringence, d
thickness, d (µm)
birefringence, d
retardation, D (nm)
23
Interference Color Chart

• Two kinds of white
• low-order
• high-order

24
Next Lecture

• How do you know which white youre looking at?
• Wedge effect, gypsum plate
• Mineral ID features sign of elongation,
  extinction type/angle
• Which is the slow ray, ? or ? ?
• Uniaxial indicatrix, conoscopic illumination
• How are biaxial minerals different?
• Biaxial indicatrix, conoscopic illumination

25
Questions to think about

• How many pleochroic colors would a mineral show
  that stayed black in XP?
• Before polarizing film, microscopes used a Nicol
  prism, made of two specially-cut pieces of
  calcite, glued together. How could you cut
  calcite to make this work?

26
(No Transcript)
27
Accessory plates

• Tell you fast vs. slow directions
• Fig. 7.21, p. 129
• Can add or subtract retardation
• Gypsum plate has D 550 nm (l)
• Mica plate has D 138 nm (l/4)
• Short dimension is always slow

28
Accessory plates

• Tell you fast vs. slow directions
• Fig. 7.21, p. 129
• Can add or subtract retardation
• Gypsum plate has D 550 nm (l)
• Mica plate has D 138 nm (l/4)
• Short dimension is always slow

29
Using accessory plates
XP

• 1) Find vibration directions, using extinction
• 2) Rotate so vibration directions are diagonal
• 3) Insert plate
• 4) If colors add, slowmineral slowplate,
  otherwise, slowmineral fastplate

D200 nm
30
Using accessory plates
XP

• 1) Find vibration directions, using extinction
• 2) Rotate so vibration directions are diagonal
• 3) Insert plate
• 4) If colors add, slowmineral slowplate,
  otherwise, slowmineral fastplate

q
p
31
Using accessory plates
45
XP

• 1) Find vibration directions, using extinction
• 2) Rotate so vibration directions are diagonal
• 3) Insert plate
• 4) If colors add, slowmineral slowplate,
  otherwise, slowmineral fastplate

q
p
32
Using accessory plates
XP

• 1) Find vibration directions, using extinction
• 2) Rotate so vibration directions are diagonal
• 3) Insert plate
• 4) If colors add, slowmineral slowplate,
  otherwise, slowmineral fastplate

q
p
33
Using accessory plates
XP

• 1) Find vibration directions, using extinction
• 2) Rotate so vibration directions are diagonal
• 3) Insert plate
• 4) If colors add, slowmineral slowplate,
  otherwise, slowmineral fastplate

p slow
q
p
D750 nm