Lecture:  Polarized light and minerals


Wednesday (last lecture)

1.     Minerals and light:
a) refraction, ray paths, & wavefronts
b) isotropic & anisotropic behavior [double refraction]
c) the optical indicatrix three types (sphere, ellipsoid of revolution, triaxial ellipsoid)

2.     Minerals in plane polarized light
a) plane polarized light is resolved by anisotropic minerals into two rays
b) relief / Becke line effect of contrasts in refractive index
c) color/ pleochroism / dispersion crystallographic controls
d) cleavage, habit, inclusions, zoning, alteration other useful features

Homework returned, please use this (and document on line for lab) to help learn minerals and formulas!

Today and next lecture (Wednesday)

1.     Minerals with cross-polars (birefringence, extinction angle[s], elongation; compare minerals in reflected light bireflectance)

2.     Minerals in conoscopic illumination (what is conoscopic illumination, interference figures, optic sign, optic angle [2V], the optical indicatrix again)

3.     A strategy for identifying minerals in thin section (Wednesday)

4.     Textural features and timing relationships in thin section (Wednesday)

5.     An introduction to mineral stability (Wednesday)

Minerals with cross polars

    What can we learn when polarized light passes through a mineral which, in turn, can split that light into two polarized components?

The way to do this is to look at the resulting light with another polarizing filter, both in direct (perpendicular or orthoscopic) illumination and in convergent (conoscopic) illumination.

The analyzer is a the second polarizing filter in a petrographic microscope. It is inserted in the optical path after the mineral being observed. The orientation of the analyzer is typically at right angles to the polarizer (first polarizing filter along the optical path).

    What would you see if you look through the scope with the light on and no section in place and then insert the analyzer?

Isotropic minerals in cross polars

Light entering isotropic minerals is not split into two rays, nor does not it have its polarization changed (BlossOC Fig. 6-5).


    What will you see when the polarizer is inserted?

    What will happen if the microscope stage (sample) is rotated? We will look at the case of fluorite using the overhead projector.

    (What is fluorite's crystal system? What common rock-forming silicate mineral group also has this crystal system? How might you use cleavage and relief to distinguish between these two in thin section?)


We saw in the last lecture that anisotropic minerals split light into two component rays. These rays vibrate in crystallographically controlled preferred directions. One ray is fast (longer wavelength) and the other is slow (shorter wavelength).

As light travels through the crystal there is a shift in the phase (position of the peaks and troughs of the waves) of these two rays. This difference is known as the retardation and is measured in nm (phase shift). See figure below (Nesse Fig. 7-14).


Subsequently as they pass out of the crystal, they recombine. The intensity of the resulting wave (for some a single wavelength) depends on the phase shift. If it is a full wavelength, then the beam has the orientation as it entered the crystal. If it is a half a wavelength, then the wave will be at 90 to the original orientation.

    Given these situations, for a single wavelength of light (monochromatic) what  will one see when the analyzer is inserted?

See figure below (Nesse Fig. 7-13)..

Origin of (birefringent) colors in cross polars

As we know, color of light is directly related to the wavelength of the light. Thus for the same retardation (difference in distance traveled by the fast and slow rays through the crystal) there will be systematic variation in the orientation of the recombined light in the beam that emerges from the crystal as a function of wavelength.

Given this fact, we will see differences in color from the original light (usually white) depending on the retardation (which is a function of the path length in the crystal and the relative indices of refraction for the fast and slow rays), some wavelengths will be fully transmitted whereas others will be partly or mostly absorbed.

For low retardations (comparable to a single wavelength) most light will base through and we see only slight changes in color (yellows or bluish grays). For intermediate retardations (2 or 3 wavelengths), certain wavelengths are cut out and the colors become more pronounced. For high retardations (4 or more wavelengths) many colors are cut out, but adjacent wavelengths are transmitted leading to bright but "muddy" colors. The colors and "orders" (number of wavelengths  retarded) are illustrated in the Michel-Levy chart (next section).


Michel-Levy chart interference colors as a function of birefringence and thickness (+ orientation)

The Michel-Levy chart (below) is a very handy summary of colors generated by different retardations in terms of (a) the difference in refractive index of the fast and slow rays (also called the birefringence; one must consider context with this term) and (b) the path length (typically the thickness of a thin section).

*** Note that there are a number of ways to use this chart:

1.     to identify minerals from their birefringence (usually combined with other properties)

2.     to estimate section thickness

3.     to constrain the birefringence of a known mineral or mineral group with variable optical properties (e.g., an amphibole) if you know the section thickness

Michel-Levy charts are found in back of Nesse and the back of Klein.

Extinction (no light passes through analyzer)

Anisotropic minerals are dark in crossed polars in certain orientations  regardless of their birefringences. These positions are positions of extinction because no light passes through.

    Why is this?

Consider what happens as the indicatrix rotates on the microscope stage. First think about sections through the crystal and its indicatrix. Light entering will be split into a fast and a slow ray unless either:

1.     the path is along the optic axis (circular section or sections of the crystal),  or

2.     plane polarized light enters parallel to one of the privileged directions (i.e., the fast or the slow direction).

In case (1) rotating the stage has no effect as all directions are the same. The resultant beam always has the same direction and thus is always cut out by the analyzer. However in case (2) the light is only cut out when the fast ray or the slow ray is oriented parallel to the polarizer (the other is at right angles). Consider the following figure for quartz (the principle is the same for all anisotropic minerals, though we would label the directions differently):

The following figure shows the orientation of the indicatrix relative to a quartz outline.


The quartz movie shows a thin section with several quartz crystals in different orientations. The first part is in plane light (can you distinguish quartz from feldspar here?); the second part show rotation with crossed polars. Which grain is oriented with the circular section in the plane of the thin section (cf. the figure above)? Is quartz pleochroic?

The gypsum plate (and analogous accessory plates)

These are accessories that are inserted in the optical path between the sample and the polarizing filter. Their function is to add a known retardation in a fixed direction so as to determine the direction of the fast and slow rays in a particular view in cross polars.

An example of this is shown here. The mineral is quartz. The first image is cross polars, the second is with the gypsum plate inserted. Most grains shift to low second-order blue color whereas a few shift to first order yellow.  This can be understood in conjunction with the Michel-Levy chart by considering that the quartz has a strong preferred orientation (most grains have have their C axes aligned in the same direction) and that 550 nm retardation is being added to the first order gray color. The grains with the opposite orientation have 550 subtracted and come out first order yellow. (Why are virtually none gray or black?)

      This is a spectacular example of a deformed quartz vein from an area in Chile where I have been doing field work. Similar textures are seen in the Santa Catalinas where quartz-rich rocks have been deformed.

Extinction angle and elongation

These properties have to do with the orientation of the fast and slow rays related to features you can see in the mineral.

Extinction angles

Parallel extinction and symmetric extinction: generally in more symmetric minerals (vibration directions are constrained by symmetry)

      Apatite is hexagonal. Crystallography requires extinction parallel to the prism (elongation) of the crystal (apatite movie).

Extinction angle (not 0 or symmetric) the angle to a characteristic direction (cleavage or long axis) at which the mineral goes extinct.

      Most amphiboles including hornblende are monoclinic (consider drawing in last lecture) and thus have non-parallel extinction in some directions and symmetric extinction in others.

Elongation (sign of elongation)

As noted above, a gypsum plate or other accessory plate adds or subtracts a known retardation to the optical path. Sign of elongation is simply whether the slow or fast direction is close or parallel to the long axis of a mineral (or a cleavage). In the quartz example above, the sign of elongation in that orientation was length slow (i.e., the slow ray is parallel to the elongation note: this can be used to show that the elongation seen in the slide is parallel to the C axis in quartz, cf. the text description of the optical properties of quartz).

Minerals in conoscopic illumination

Another powerful way of examining minerals in thin section is by using convergent light rather than parallel light. This is known as conoscopic illumination and is generated by inserting the condensing lens (part of the microscope's substage) into the optical path. In combination with the Bertrand lens this allows one to effectively see the nature of retardation across a significant part of the crystal's indicatrix. The image generated is known as an interference figure.  This section focuses on the nature and use of interference figures which are of great practical value in the identification of minerals in thin section.

The following sketch shows elements of the generation of interference figures. Parts are summarized in the next section.

Interference figures

Interference figures consist of three parts:

1.     isochromes zones of constant color corresponding to the projection of lines of equal retardation (see Nesse Fig. 7-36 above)

2.     isogyres dark zones that correspond to preferred vibration directions in the crystal and are thus extinct

3.     melatopes dark spots at key points within the isogyres that correspond to the optic axis(axes)

These are illustrated below:

Below: a centered uniaxial interference figure. The isochromes are colored, the isogyres are black and the melatope (optic axis) is at the center of the cross.

Formation of isogyres is illustrated below.

Quartz movies

Two quartz isogyre movies show the uniaxial interference figure for the central grain seen in the quartz movie above (the dark one). The first movie showing the interference figure is without the gypsum plate. The second interference figure movie is with the gypsum plate. The colors are a bit washed out (auto exposure on the camera), but you should be able to see the isogyres, melatope, and the blue yellow(looks red here) contrast that helps one determine optic sign (described below).

Below an interference figure for a biaxial mineral (at extinction). The two thin spots in the isogyres are the position of the two optic axes. Note how the isochromes surround them.

The next figure shows a similar biaxial mineral at 45 off extinction. Note the isogyres have split but the optic axes are still at the center of the isochromes.

Return to the indicatrix

Depending on the ratios of the principal axes of the indicatrix,  minerals are known as optically positive or optically negative. For biaxial minerals, the angle between the optic axes (cf. Nesse Fig. 7-27 see the last lecture for this figure) is called 2V. (There is an acute and obtuse 2V which add to 180; we are generally only interested in the acute angle which spans what is called the "acute bisectrix.")

Optically positive (designated "U+" or "B+") In this situation, for uniaxial minerals the indicatrix is elongated vertically (the highest index is along C; i.e., a football shape). For biaxial minerals, the acute bisectrix contains gamma (the highest index) and the other two are close to one another (alpha and beta). In the case of optically negative minerals, the uniaxial indicatrix is squashed (Frisbee-like). For biaxial beta and gamma are closer together and the acute bisectrix includes alpha, the lowest index.

Determination of optic sign and, for biaxial minerals, optic angle (2V)

Telling the difference between uniaxial and biaxial minerals

    How do you tell if a mineral is isotropic?

    From the above discussion, how would you use conoscopic examination to distinguish between the two?

In most cases, interference figures will be off-center. In other words, one of the principal directions is not coincident with the microscope axis. In this case, it can be a bit tougher to tell. If the figures are reasonable close to centered then it may be obvious. If they are far off center, then a useful clue is to see if the isogyres cross the cross-hairs are angled angle (biaxial case) or if they are parallel to the cross-hairs (uniaxial case). See next illustration for the uniaxial example.

Determination of sign

This is done by inserting the gypsum plate (or similar accessory) when looking at the interference figures.

Uniaxial case The crystal is uniaxial positive (U+) if colors add in the NE and SW quadrants (as in the figure below). It is negative (U-) if the colors add in the NW and SE quadrants. The figure below shows the U+ case for a relatively low birefringence mineral like quartz.

Biaxial case A similar rule holds for biaxial minerals: with the crystal turned 45 degrees from extinction, the crystal is biaxial positive (B+) if colors add outside the isogyres in the NE and SW quadrants. It is negative (B-) if the colors add in the NW and SE quadrants. The figure below shows the B- case for a relatively low birefringence mineral. (You can see the analogy in sign if you imagine 2V going to 0 at which point the isogyres would merge to look like the U- case.)

Determination of 2V in biaxial minerals

There are two approaches to determine 2V (if needed). The easiest (and the only one we use here) is to find an optic axis figure (i.e., look for a grain that is always dark in cross polars). In conoscopic illumination, the melatope (optic axis) will be at the cross-hairs and the curvature of the isogyres is a measure of 2V as indicated in the figure below (this can vary with the microscope, but most are standardized to the same values).

The second approach is to find an acute bisectrix figure and measure the distance between  between the melatopes at 45 from extinction. It is good to be aware of this method, but it is more difficult to apply (described in optical mineralogy books).

A strategy for the study of minerals in thin section

Using these tools, we will develop a recipe for studying minerals using optical techniques in thin section. With experience it is often possible to identify minerals almost instantly, yet in many cases even expert petrographers (as well as the rest of us!) need to use the whole range of tools described above.

For next time:  Reading

Same material for this and previous lectures + lab

Klein 292-309 (Optical Microscopy through reflected light), or Nesse  Chapter 7 (p. 114-159) [coverage of optics in Nesse is superior to that in Klein]

Klein Chapter 4 discusses mineral stability and phase diagrams -- we will begin looking at this in the next lecture (particularly in following lectures)

Be prepared for:

    Discussing a strategy for identifying minerals.

    What other features we want to observe in thin section.

Review material

Reminder of GEOS 251 notes and lectures

- Press et al. (2004) Understanding Earth, Freeman Chapter 4 / Rocks and rock cycle

- 251 notes (on-line: http://www.geo.arizona.edu/geo2xx/geo251/)

- Lecturs 5 (pdf file) covers rock cycle

- Quicktime movies of GEOS 251 PowerPoint lectures linked from class web page