Uniaxial opics

1
Uniaxial opics

• Nesse, 1991
• Chapter 6, page 53 to 76

2
REVIEW

• An indicatrix is a geometric figure that shows
  the index of refraction and vibration direction
  for light passing in any direction through the
  material
• IMPORTANT Indicatrix is constructed so R.I.s
  plotted as radii that are parallel to the
  vibration directions of the light
• Simplest example Isotropic Indicatrix- the
  velocity of light is the same in all directions
  as it passes through a substance ie a sphere
• This is exhibited by glasses
• minerals of the cubic system eg Garnet

3
Optical properties of uniaxial minerals

• UNIAXIAL Minerals eg calcite
• Two images are produced by double refraction,
  each image composed of PPL vibrating at right
  angles to each
• If the rhomb is rotated, one image is stationary
  thus behaves like isotropic material (known as
  ORDINARY RAY, ?)
• one moves around, very different from what was
  expected in an isotropic material (known as
  EXTRAORDINARY RAY , e )

4
Optical properties of uniaxial minerals

• The ordinary ray vibrates perpendicular to the
  c-axis
• The extraordinary ray always vibrates
  perpendicular to the ordinary, so it vibrates in
  a plane that contains the c-axis

5
Optical properties of uniaxial minerals

• In calcite the refractive index of the
  extraordinary ray, ne is smaller than that of the
  ordinary ray, nw.
• Thus nw gt ne
• This is called OPTICALLY NEGATIVE or the negative
  optic sign.
• In the opposite case, when ne gt nw the mineral is
  called OPTICALLY POSITIVE or positive optic sign

6
Uniaxial indicatrix

• It is important to know where are your indices of
  refraction within a crystal and what are their
  values
• We already know that the nw vibrates
  perpendicular to the c-axis and the ne in the
  plane that includes the c-axis
• The value of the refractive index varies between
  ne and nw and intermediate values are referred to
  by ne
• IMPORTANT In anisotropic minerals, only
  specific crystallographic sections are isotropic,
  the general rule is double refraction. The
  direction perpendicular to an isotropic section
  is called an optic axis.

7
UNIAXIAL MINERALS
UNIAXIAL ve

• Geometric figure is constructed called
• UNIAXIAL INDICATRIX
• All light traveling along the Z-axisoptic axis
  has nw, whether it vibrates parallel to X or the
  Y-axis
• So X-Y plane of indicatrix must be a circle (and
  mineral is uniaxial positive)

UNIAXIAL -ve
8
Uniaxial indicatrix
?gt? Uniaxial ve

• Other planes that contain the c-axis are called
  principal sections
• Relationship between crystallography of mineral
  privileged directions (R.I.s) best viewed with
  uniaxial indicatrix

?lt? Uniaxial -ve
9
Uniaxial indicatrix

• When nw gt ne optically negative
• The indicatrix is oblate ellipsoid
• Or when ne gt nw optically positive
• The indicatrix is prolate ellipsoid

ne
ne
10
Uniaxial indicatrixBirefringence and
Interference Colors

• Case 1 Normal incidence on a sample cut
  perpendicular to the c-axis
• Circular section nw
• When placed between crossed polars the light is
  entirely absorbed
• Section stays dark on rotation of stage, acts as
  if isotropic

11
Uniaxial indicatrixBirefringence and
Interference Colors

• Case 2 Mineral cut parallel to optic axis
• Indicatrix section is a principal section with
  the axes equal to ne and nw
• Section called optic plane
• Incident ray split into two rays vibrating
  perpendicular to optic axis

• So Birefringence is ne - nw which is maximum or
• highest interference color

12
Uniaxial indicatrixBirefringence and
Interference Colors

• Case 3 Mineral is cut in random direction
• Ordinary ray has refractive index nw
• Extraordinary ray has an index ne intermediate
  in value
• This crystal will show a birefringence color
  lower than the maximum
• ie partial birefringence

13
Uniaxial indicatrixBirefringence and
interference colors

• We can use this technique the other way around.
• We can use the interference colors to find the
  correct section of the indicatrix in a section
  with randomly oriented mineral grains.

14
Uniaxial indicatrixBirefringence and
Interference Colors

• When observing randomly oriented grains in thin
  section
• To find the grain with nw look for the isotropic
  section section perpendicular to c
• To find the grain with ne and nw look for the
  section with the highest interference colors
  section parallel to c or // optic plane

15

• Extinction in tetragonal minerals Optic axis is
  parallel to 4-fold symmetry axis

Isotropic section
Section with highest interference colors
6.10
16

• Extinction in hexagonal minerals Optic axis is
  parallel to 6-fold symmetry axis

Isotropic section
Section with highest interference colors
6.12
17
Interference figures
An interference figure is optical phenomenon
observed through a polarizing microscope when it
is arranged conoscopically (ie strongly
converging light).

• How to make an interference figure
• 1/ Focus on mineral grain, first with low power
  and then with high power objective
• 2/ Flip in the condenser
• 3/ Cross the polars
• 4/ Insert Bertrand lens

18
Interference figure

• When the optic axis of the grain is perpendicular
  to the stage (or section perpendicular to c-axis)
• 1/ Centered uniaxial interference figure

Melatope
Isochrome
Isogyre
19
2/ Off-Centered Uniaxial Interference Figure

• Section not perpendicular to c-axis
• Not parallel to optic plane
• Somewhere in between ie partial birefringence

• 3/ Flash Figure Broad fuzzy indistinct cross
• Section of mineral contains c-axis and the Optic
  Axis is parallel to microscope stage
• Such a grain exhibits maximum birefringence in
  thin-section

20
Interference figures

• Interference figure in tetragonal minerals

Isotropic section Centered uniaxial
Section with highest interference colors - Flash
Figure
Section with intermediate interference
colors Off-centered uniaxial interference figure
6.10
21
Interference figures

• Extinction in hexagonal minerals

Isotropic section Centered uniaxial
Section with intermediate interference
colors Off-centered uniaxial interference figure
Section with highest interference colors - Flash
Figure
6.12