Lecture Test 3

Orthoscopic observation

uses parallel rays to create a realistic flat image

Conoscopic observation

uses converging rays to observe optical patterns produced by minerals

• condenser

Microscope tube

straight metal tube that separates the objective from the ocular

Oculars

consists of a tube that fits into the tube of a microscope, usually with a small screw to hold it in a fixed position.

• always contains cross-hairs

• may or may not contain micrometer

• assembly consists of 2 plano-convex lenses

Plano-convex lens

a beam of light travelling parallel to the lens axis and passing through the lens will be converged (or focused) to a spot on the axis, at a certain distance behind the lens (known as the focal lenth)

Huygenian ocular

ocular where (-):

• both lenses are made of some kind of glass

• separated by distance (F1 x F2)/2

• planar surfaces face observer

• field diaphragm and cross-hairs lie in the focal plane

• minimum spherical aberration

Spherical aberration

a lens defect whereby the lens fails to bring the focus at the same point the light passes through its periphery and light that passes through its center.

alt. def:

light rays passing through periphery of lens come to focus at a different point than the light rays passing through the center

Ramsden ocular

ocular where:

• both lenses are of equal F

• separated by (F1 + F2)/3

• convex surfaces face each other

• the field diaphragm and x-hairs lie in the focal plane of ocular between the field lens

• best for quantitative measurements and photomicroscopy

Bertrand lens

small achromatic doublet designed to limit the effects of chromatic aberration.

• achromatic doublet is made of 2 lenses:

  • 1 concave made of flint glass (high dispersion)

  • 1 convex made of crown glass (low dispersion)

• chromatic aberration of one is countered by the other

Chromatic aberration

lens defect resulting in failure to focus light of different wavelengths at the same point.

Analyzer/Upper Nichol

Typically fixed to pass only light wave components that vibrate in an E-W plane and is used in combination with the lower polarizer

Accessory opening

Below the analyzer, where you insert accessory plates (commonly gypsum)

Objective lens

most critical part of the microscope with the main functions of magnification and resolution. It’s a complex system of lens elements whose quality is determined by the degree to which it corrects spherical and chromatic aberration.

Magnification

• low power: rock textures

• medium power: most optical properties

• high power: interference figures/small features

Resolution

Qualitative ability of the objective lens to reveal fine detail; quantitatively a measure of the smallest distance at which 2 points can be seen as clearly separated

Free working distance (FWD)

distance between the lens and cover glass when subject is in clear focus

Depth of focus

the vertical distance that is simultaneously in focus; decreases with increasing magnification

Microscope stage

Rotated and is marked with degrees.

Mechanical stage

screw firmly to microscope stage and rotates with it; it permits a glass slide to be moved smoothly on the microscope stage

Condenser

part of substage assembly made of 2 simple lenses; it supplies a cone of light (conoscopic illumination) just large enough to fill the front lens of the objective completely, thereby giving maximum illumination.

Iris or aperture diaphragm

part of substage assembly which controls the size of the cone of light passing up through the microscope; closing it decreases light and increases contrast of the image

• close iris when observing relief, becke line, and depth of focus)

Interference phenomenon

in most cases, when an anisotropic mineral is viewed under the microscope between crossed polarizers, light passes the upper polarizer and the mineral displays colours called interference colours, which are produced as a consequence of double refraction

Development of retardation

Plane polarized light entering an anisotropic mineral is split into 2 rays that vibrate at right angles to each other and have different indices of refraction (velocities), i.e. and slow and fast ray. In the time is takes the slow ray to pass through the mineral the fast ray will have already passed through the mineral, plus an additional distance called retardation (Δ)

• magnitude of the retardation depends on the thickness of the mineral (d) and the index of refraction of the slow ray

  (ns) and the fast ray (nf) in the mineral

Interference colours

Result when the slow and fast rays reach the upper polarizer and are resolved into its vibration direction; determined by magnitude of retardation and whether the slow and fast rays are in or out of phase

Birefringence (δ)

• depends on the direction of light through a mineral

• e.g. perpendicular to an optic axis δ = 0, parallel will show max, most directions show intermediate

What happens when the slow ray is retarded an integer number of wavelengths relative to the fast ray (Δ=nλ)?

the components of the two rays resolved into the vibration direction of the upper polarizer and are of equal magnitude but in opposite direction, thereby canceling out each other, therefore no light passes the upper polarizer and the mineral appears black

What happens when the slow ray is retarded an integer number of wavelengths relative to the fast ray (Δ=1/2λ)

The 2 rays resolved into the vibration direction of the upper polarizer, but the resolved components are both in the same direction, so the light constructively interferes and light passes the upper polarizer with maximum light intensity

Polychromatic Illumination

With white light all wavelengths are present and each is split into slow and fast rays. Some wavelengths reach the upper polarizer and cancel each other out, but others are transmitted, which produces what we perceive as interference colours

• Therefore, if a quartz wedge is placed between crossed polars we see a range in interference colours called the interference colour sequence

Accessory plate

Determines the direction of fast (ω) and slow (ε) rays passing through a mineral, which is used to find the sign of elongation and the optic signs

Determining the sign of elongation

1. find an elongate mineral

2. rotate stage until mineral is extinct

3. rotate stage 45° clockwise

4. record the interference colour

5. insert the gypsum plate

   • if colour increases - slow on slow - length slow

   • if colour decreases - fast on slow - length fast

Optical indicatrix

Is an illustration of how the index of refraction (n) of a mineral varies with the vibration direction of a light wave in a crystal

Indicatrix sections

represents a section with a particular orientation through a crystal

Uniaxial indicatrix

1. Light entering a birefringent crystal is refracted into two rays ω and ε with different indices of refraction

   • ε rays: the ray path and wave normal do not coincide

   • ω rays: the ray path and wave normal do coincide

2. No double refraction is observed when light passes along the c-axis of a hexagonal or tetragonal crystal; nω = nε

3. The ω-ray vibrates perpendicular to the c-axis

4. The ε-ray vibrates parallel to the c-axis

5. For light vibrating at a random angle to the c-axis, the n lies between nω and nε

6. Therefore, we can construct an indicatrix for a uniaxial mineral:

   • It is an ellipsoid

   • One axis = nε = c-crystallographic axis = optic axis

   • At right angles to this is nω , which occupies all vectors perpendicular to

   c-axis, and describes a circle

7. Optic axis is the direction perpendicular to the circular cross-section

   • i.e., equivalent to the c-axis

If nε > nω (in uniaxial indicatrix)

the extraordinary rays are slow and the mineral is optically positive (+); the indicatrix is a prolate spheroid

If nε < nω (in uniaxial indicatrix)

the extraordinary rays are fast and the mineral is optically negative (-); the indicatrix is an oblate spheroid

Basal / optic axis / circular section

a section cut perpendicular to the optic axis and it is a circle

• Light propagating along c-axis therefore it is not double
  refracted because is following optic axis

• Isotropic; best for interference figure

Principal section / principal plane/ principal ellipse

Section cut along the optic axis; therefore it intersects the indicatrix as an ellipse whose semi-axes are equal to nε and nω

• Maximum birefringence- best for observing
  sign of elongation

Random section

a section cut at a random angle (Θ) to the optic
axis; it is an ellipse whose semi-axes are equal to nε’ and nω , where nε’ is between nε and nω

• intermediate birefringence

Interference figures

Interference figures are formed near the top surface of the objective lens and consist of a pattern of interference colours called isochromes on which dark bands called isogyres are superimposed

• Their behaviors as the stage is rotated depends on the orientation of the mineral grain and whether the mineral is uniaxial or biaxial.

Uniaxial

anisotropic minerals with one direction
of apparent isotropy; one optic axis

• hexagonal, trigonal, and tetragonal crystal systems

Biaxial

Minerals with 2 optic axes; 2 directions along which the
light shows no birefringence and vibrates in a circular section with a unique constant refractive index (known as β)

How to view an interference figure

1. Focus on a single grain with the highest powered objective lens

2. Flip in the auxiliary condensing lens. Refocus if needed and open the aperture diaphragm. Insert the upper polarizer.

3. Insert the Bertand lens. Interference figures can also be observed without the Bertrand lens by removing the ocular and looking straight down the microscope tube

Optic Axis (O.A.) Interference Figures

produced if a uniaxial mineral’s optic axis is perpendicular to the microscope stage

Melatope

marks the point of emergence of the optic axis

• uniaxial have 1, biaxial have 2

Formation of isochromes

1. auxillary condensing lens provides strongly convergent light that passes through the mineral and is collected by the objective lens

2. light following path 1, parallel to the OA is not split into 2 rays and exits the mineral with 0 retardation to form the melatope

3. light following path 2 has moderate retardation because the value of nε is close to nω

4. light following path 3 (at a greater angle to the OA) encounters higher birefringence and must travel a greater distance through the mineral because the retardation is proportionally greater

5. Because optical properties are symmetric about the OA, rings of equal retardation and interference colour are formed about the melatope

6. minerals that are thick or have high birefringence show more isochromes than thin or low birefringence minerals

Formation of isogyres

• form where vibration directions in the interference
  figure are N-S and E-W

• they represent areas of extinction

• ω rays vibrate parallel to lines of latitude on the
  indicatrix and tangent to the circular
  isochromes

• ε’ rays vibrate parallel to lines of longitude
  on the indicatrix and along radial lines symmetric about the
  melatope

Off-Centre Optic Axis Figure (uniaxial)

interference figure will no longer be centered in the FOV because the optic axis is inclined within ~30° from the vertical

• can still be used for optic sign

Off-centre figure

the optic axis is incline >30° from the vertical so the melatope is not in the FOV

• can’t be used for optic properties or optic sign

Optic Normal or Flash Figures (uniaxial)

produced if mineral grain is oriented with its optic axis parallel to the microscope stage; characterized by broad fuzzy isogyres that occupy nearly the entire field of view

• display max interference colours

2V

angle between the 2 optic axes of a biaxial mineral

Optic axis figure (biaxial)

section is cut perpendicular to an optic axis

• crystal viewed down OA

• grain displays 0 or min birefringence

• melatope (OA) centered in FOV

• if 2V < 30°, other melatope may be in FOV

• if 2v > 60°, other melatope not in FOV

Acute bisectrix figure (biaxial)

acute bisectrix is perpendicular to the microscope stage

• grains display intermediate retardation

• if 2v < 60°, the 2 melatopes will be in FOV

• isogyres change as stage is rotated (join then separate)

• isochromes form oval or figure 8 about melatope

• you can estimate the 2V angle based on separation of isogyres

Obtuse bisectrix figures (biaxial)

obtuse bisectrix is perpendicular to the microscope stage

• grains display intermediate retardation

• melatopes outside FOV because angle between Bxo and OA > 45°

• broad diffuse cross of isogyres visible in one position

Off-center figure (biaxial)

rotates off center and usually can’t be used to determine optic sign or 2V

Optic normal figure/flash figure (biaxial)

optic normal is perpendicular to the stage, optic plane is parallel to stage, so you see a blobby figure