Interference Figures

Steven Dutch, Natural and Applied Sciences, University of Wisconsin - Green Bay
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What Interference Figures Are

The optical properties of minerals vary with direction. It would be nice if we could somehow view the overall optical properties of a mineral in many directions at once. We do that by generating an interference figure.

Assume we have a thin section with a grain oriented so that we are looking down an optic axis. In that direction, recall, the grain has zero birefringence. If we pass a cone of converging light through a specimen as shown above and view the exiting light, two things will happen

How to Create an Interference Figure

With the Unaided Eye

If a grain is big enough, the interference figure can actually be seen with the unaided eye. One easy way is to take a moderately thick but still clear sheet of mica, sandwich it between two crossed polarizers, then look at a blank white wall or the sky. The interference figure is easily seen. This is a biaxial figure - the mineral has two optic axes. Uniaxial figures are harder to make only because there are no uniaxial minerals with the easy and correctly oriented cleavage of mica. A thin slice of quartz or calcite, cut perpendicular to the three-fold axis and sandwiched between polarizers, will work.

The Ping-Pong Ball

One of the niftiest manufacturers' promos I ever got was half of a ping-pong ball glued to a polarizer. Put a sheet of mica on the stage of a microscope, turn the illuminator up and put the ping-pong ball on top with the attached polarizer crossed. The interference figure is projected neatly onto the ball!

With the Microscope

Muscovite and biotite will give excellent interference figures. Simply place a cleavage flake on a slide and practice getting interference figures until you become proficient.

What To Do Why You Do It
Find a grain that has very low interference color in all orientations, black if at all possible You are trying to locate a grain with its optic axis perpendicular to the slide. You want to be looking along the optic axis, or as close as you can possibly get. How close that is depends on the birefringence of the mineral. For quartz, the grain must be almost black at all times, for olivine, first-order gray will do. For calcite, any recognizable interference color will probably work. Try to be at least in the lower 10% of the mineral's color range. Sometimes you just can't do it with a given thin section, especially if the mineral you're dealing with has only tiny grains or very few of them.
Raise the substage condenser as far as possible so it is immediately under your slide Create a cone of converging light passing through the specimen in as many directions as possible
Go to high power You want to zero in on the grain and eliminate competing stray light from other sources
Bring the objective as close to the slide as you can get it You want to capture as much of the now-diverging light as you can
Flip in the Bertrand Lens The light is diverging strongly, unlike normal viewing, and cannot be focused like normal light. An extra lens is needed to focus the light. This is the Bertrand Lens. It is located above the upper polarizer but its location and means of employment vary from one instrument to the next. In some instruments it flips in and out of place with a lever, in others it is located on a rotating wheel.

What You See Under The Microscope

Isotropic Minerals

Isotropic minerals (isometric or noncrystalline) are black in all orientations. They do not give interference figures (do you really need one?)

Uniaxial Minerals

The point in the interference figure corresponding to the optic axis, whether it's uniaxial or biaxial, is always black. There are two reasons why:

This point is called the melatope (Greek: black place)

uniax1.jpg (30808 bytes) At left is an actual photograph of a uniaxial interference figure. This is a specially-ground slice of calcite. An interference figure for quartz would show isochromes much more widely spaced. In a typical thin section, an interference figure for quartz would show the isogyre but only the first-order white isochrome.

Biaxial Minerals

Optic Axis Figures

The figures described above are called optic axis bisectrix figures. That is, you are looking down a line that bisects the angle between the optic axes. This is actually the best orientation for determining the optical properties of the mineral.

If you view straight down a biaxial optic axis, the isogyre will always pass through the center of the field. The other optic axis always is in the convex direction of the isogyre. If the angle between the optic axes (the so-called 2V angle) is 90 degrees, the other optic axis is equally far away in either direction, and the isogyre appears to be a straight line that rotates as you rotete the stage. The other optic axis in this case lies on a line perpendicular to the isogyre.

Oblique Biaxial Figures

The interference figure described above is actually what you get by looking halfway between the optic axes, a so-called acute bisectrix figure. The retardation in this case is not exactly zero. However, it's impossible using simple inspection alone, to tell grains with this orientation from other differently-oriented grains with the same retardation.

If you look exactly down a biaxial optic axis, you may still see enough of the entire figure to orient yourself. For large 2V, though, you will not. You will only see part of one hyperbola. If 2V = 90 degrees, the isogyre looks like a rotating straight line. For other values it curves. The other optic axis is always in the direction of the bow of the curve.

At very large angles to the optic axes, the hyperbolas are very close to the polarizer directions and very diffuse. It is nearly impossible to tell whether the figure is uniaxial or biaxial in this case.

Flash Figures

If you look at a uniaxial or biaxial mineral perpendicular to the optic axes, a flash figure results. Grains with this orientation have the maximum interference color for the material.

For a uniaxial mineral, one privileged direction always points toward the optic axis. For a biaxial mineral, the privileged directions bisect the angle between the light ray and the optic axes. Either way, an interference figure viewed perpendicular to the optic axis has all its privileged directions parallel.

                                       OA1*                       *OA2
                                              .               .
                                                  .       .
     *-------- --+-- --------*                      --+--   <------+------>
                                                  .       .
                                              .               .
     OA-----180 degrees-----OA         OA2*                       *OA1

              Uniaxial                             Biaxial

What happens is that when the privileged directions are parallel to the polarizer, the field goes black. This happens very quickly, hence the term flash figure.

Another way to picture this situation is this: looking at right angles to the optic axis is the same as a 2V of 180 degrees. The flash figure behaves like a biaxial figure with two hyperbolas merging to form a cross and then diverging. However, the cross is so large it fills the field and the hyperbolas break apart and move very quickly. The figure is so large and diffuse it is hard to view the details.

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Created 31 Oct 1997, Last Update 16 December 1999

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