Light waves are transverse waves that vibrate perpendicular to the line of propagation.

v = lf, where v = velocity; l = wavelength; f = frequency

Light waves may interfere constructively or destructively.

Monochromoatic light is light of a single wavelength. Polychromatic light (white light) contains many wavelengths. For our purposes light is measured in millimicrons (or nanometers). One nanometer is 10-9 m.

The refractive index of a substance is defined as the velocity of light in a vacuum (v) divided by the velocity of light in the substance (V); n = v/V. When light travels from one medium to another it is bent, according to Snell's Law, which states:

n2 / n1 = sin i / sin r , where i and r are the angles of incidence

(measured from the normal) and of refraction (measured from the normal), respectively. In passing from a medium of lower index to a medium of higher index, a light ray is bent toward the normal.

Plane polarized light is light constrained to vibrate in a single plane. The polarizer of a microscope provides plane polarized light with which to view minerals. The analyzer of a microscope is second polarizing plate set in the optical column at right angles to the first; consequently, when the polarizers are crossed, no light passes through the optical column.

Relief is the degree of visibility of a transparent particle in a medium under the microscope. Commonly mounting media for thin sections have n near 1.54, so we measure relief with respect to this value. We express relief quantitatively as low, moderate, high, and extreme.

The Becke Line is a thin bright line of light at the interface between a mineral fragment and an immersion medium. As the distance between the objective and the fragment is increased, the Becke Line moves into the medium with the higher refractive index.

Dispersion is a term that refers to variation of refractive index with wavelength.

In anisotropic media, the birefringence is defined as the difference between the largest and smallest refractive indices. d = (n2-n1)

This difference gives rise to a lag of one ray compared to the other, depending on the thickness of the section, and this lag is spoken of as retardation, D. D = t (n2-n1) = t d. Retardation is measured in millimicrons, and is manifested by interference colors. The interference color sequence is divided into orders (first, second, third, etc.) at 550mm intervals. Remember that the first order has no blue, and higher orders have no white. "High-order" white is distinct, and you should now be able to recognize (and describe) it.

Isotropic substances: Liquids (most), gases, isometric minerals, glasses.

Light moves with the same velocity in all directions through isotropic media. They are characterized by a single refractive index, n. Under crossed polarizers, no light is transmitted. If colored, they are characterized by a single color only (not pleochroic). Identification depends on observation of relief, hence n; crystal shape; color; cleavage; associated minerals.

Isotropic minerals and mineraloids that you should know: Volcanic glass, fluorite, sodalite, analcime, hauyne, garnet, spinel, chromote, perovskite. Leucite (1,2,3) is often considered isotropic, although it is weakly anisotropic.

Anisotropic substances: Those substances that transmit light with different velocities in different directions, and include all substances that crystallize in systems other than the isometric system.

Uniaxial substances are those that crystallize in the tetragonal and hexagonal systems. They are characterized by having two principal refractive indices, ne, and nw and a single optic axis. Vibration directions and refractive indices can be sketched out as an indicatrix, and ellipsoid of rotation, constructed by placing ne on the y-axis, and nw on the x-axis, computing intermediate values between ne and nw rotating the resulting curve through 360o. For positive crystals, the ellipsoid is prolate (ne>nw); for negative crystals, the ellipsoid is oblate (nw>ne).

In convergent light, a centered optic axis figure is obtained on sections that appear isotropic under crossed polarizers; these are sections cut normal to the c-axis of the crystal. On insertion of the accessory plate (550mm), colors rise in the NE quadrant if the mineral is positive, but fall in the NE quadrant if the mineral is negative.

In sections parallel to the optic axis (that is cut so that the optic axis lies in the plane of the section), flash figures are obtained. These are useful for determining optic sign, as the c-axis lies in the two quadrants where the figure exits the field on rotation. It is a simple matter to determine whether the c-axis is fast (negative) or slow (positive).

Important uniaxial minerals that you should know are:

Positive--quartz (1,2,3,4,5,6) , brucite, zircon, rutile

Negative--Calcite, dolomite, nepheline (1,2), beryl, tourmaline (1,2), idocrase (vesuvianite)

In addition to relief; crystal shape; color; cleavage; and associated miners, uniaxial minerals are characterized by their optic sign, birefringence, pleochroism, and sign of elongation. Careful with this last one.