Geo 406 Lecture 04 – Pleochroism, Interference, Double refraction

Reading: p. 37-39, 51

next: Ch. 5

Goals

Understand the interaction of light and anisotropic minerals

Understand pleochroism

Understand interference colors

Understand Michel-Levy chart

Today’s 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?

Background

Vectors

Light as wave

Interference (2D)

Interference (3D)

Polarization

Light can be constrained to vibrate in a particular plane

 

When two light rays combine, their vibration vectors add (vector-wise)

Polaroid film (in the polarizer & analyzer on your scope) absorbs light vibrating perpendicular to it’s direction

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

Double refraction

Calcite demo

One ray takes unexpected path through crystal (extraordinary, e´ or E´ ray)

wave normal not || ray propagation direction

Special direction where this doesn’t happen: optic axis

calcite n_w = 1.658 and n_e´ = 1.486

which image looks “deeper”?

Double refraction - movie

Pleochroism

Two rays are absorbed differently

can show different color (distribution of wavelengths)

or intensity of color

Isometric - no pleo.

Hexagonal, tetragonal - 2 “end-member” colors

Tourmaline Movie

Triclinic, Monoclinic, Orthorhombic - 3 “end-members”

Glaucophane movie

Pleochroism

Isometric - no pleo.

Hexagonal, tetragonal - 2 “end-member” colors

Triclinic, Monoclinic, Orthorhombic - 3 “end-members”

Recap

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

Retardation – PowerPoint

fast & slow rays are 45° from polarizer

D = d (n_s - n_f)

distance, nm

Interference

Retarded rays get vector-combined in analyzer (“XP”)

If D=nl, no ray passes analyzer

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 (n_s - n_f)

If the new vibration direction is 0° or 180° from the incoming, the ray is canceled at the analyzer (upper polar)

when D=l, or D=2l , or D=3l , or D=4l , etc.

Extinction

When fast or slow direction || polarizer

will occur every 90° of stage rotation

Calcite demo

Interference Colors

What changes for other colors (wavelengths)?

D = d (n_s - n_f)

Interference Colors

Story above was for one wavelength (color) of light

Retardation distance (D) is ~same across colors, but:

D = n l -> no ray (rotation = 0° or 180°)

D = [n l - (l/2)] -> max.ray (rot.=90°, 270°)

Certain wavelengths get blocked at analyzer, others pass

produces an “interference color”

Thickness effect

D = d (n_s - n_f)

quartz wedge demo

d = (n_s - n_f) = 0.009 (a small value)

shows change in set of transmitted wavelengths (i.e., color) with increasing retardation, D

Birefringence effect

D = d (n_s - n_f) = 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 (=n_s-n_f) ranges from 0 to a maximum

0 is looking down optic axis

Interference Color Chart

range of colors - same as quartz wedge

measuring birefringence

Interference Color Chart

Orders

Every 550 nm (≈ l_blue)

Interference Color Chart

Two kinds of white

low-order

high-order

Next Lecture

How do you know which “white” you’re looking at?

Wedge effect, gypsum plate

Mineral ID features: sign of elongation, extinction type/angle

Which is the slow ray, w or e ?

Uniaxial indicatrix, conoscopic illumination

How are biaxial minerals different?

Biaxial indicatrix, conoscopic illumination

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?

 

 

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

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

Using accessory plates

1) Find vibration directions, using extinction

2) Rotate so vibration directions are “diagonal”

3) Insert plate

4) If colors “add”, slow_mineral || slow_plate, otherwise, slow_mineral || fast_plate

Using accessory plates

1) Find vibration directions, using extinction

2) Rotate so vibration directions are “diagonal”

3) Insert plate

4) If colors “add”, slow_mineral || slow_plate, otherwise, slow_mineral || fast_plate

Using accessory plates

1) Find vibration directions, using extinction

2) Rotate so vibration directions are “diagonal”

3) Insert plate

4) If colors “add”, slow_mineral || slow_plate, otherwise, slow_mineral || fast_plate

Using accessory plates

1) Find vibration directions, using extinction

2) Rotate so vibration directions are “diagonal”

3) Insert plate

4) If colors “add”, slow_mineral || slow_plate, otherwise, slow_mineral || fast_plate

Using accessory plates

1) Find vibration directions, using extinction

2) Rotate so vibration directions are “diagonal”

3) Insert plate

4) If colors “add”, slow_mineral || slow_plate, otherwise, slow_mineral || fast_plate