CHAPTER I.

INTRODUCTORY OPTICS FOR OPTICAL MINERALOGY.

The object of this introduction is merely to give a practical discussion of elementary optics, as applied to optical mineralogy,[3] and no elaborate discussion of this important subject will be attempted. The explanations will be made as simple as possible, and, in most cases, only the optical phenomena will be described without entering into a theoretical discussion as to the cause of these phenomena.

_Light_[4] may be regarded as transmitted in straight lines by vibrations of the “ether,” taking place at right angles to the direction of transmission.

_Ordinary light_ is light with the ether vibrations in all possible directions, the path described by any particle of ether constantly changing.

_Plane polarized light_ is simply light with the ether vibrations all _parallel_ to one plane passing through the direction of transmission.

By experiment it has been proved that there exists a very close relation between the optical properties of crystals and their other physical properties, such as form, color, transmission of heat, etc. Therefore it is often possible, by a careful optical investigation of a crystal section, to determine important crystallographic facts, even in the absence of any distinct outline.

The Effects Produced by Crystals on Transmitted Light.

Consider that a series of optical tests are made on all possible sections[5] of crystals in the six systems, and the manner in which these crystals affect transmitted light ascertained.

▄Isotropic Crystals▄: It will be found that all sections of _Isometric_ crystals transmit light with equal velocity in all directions; that is, the crystals are optically equivalent in all directions and, hence, can produce no double refraction.[6] In these crystals any section, however cut, will transmit all the rays of light, incident to the surface at right angles, with no change.[7] The same is true of _Amorphous_ bodies, glass, etc., unless they have been subjected to strains or peculiar conditions during cooling. A _single image_ is seen through these isotropic sections.

[Illustration:

FIG. 1. ]

▄Anisotropic Crystals▄: It will also be found that nearly all sections (the exceptions being given later) of crystals in the remaining five systems, produce quite a different effect on transmitted light. In these crystals the velocity of transmission of light varies with the _vibration direction_ of the light rays. This property, called _double refraction_,[8] seems to result from the power of resolving a ray of ordinary light, with ether vibrations in all directions, into two rays with ether vibrations in planes at right angles to each other; the two resulting rays traversing, usually, divergent paths in passing through the section.

The mineral calcite (Iceland spar) exhibits this property to a marked degree, and in certain sections will show a _double image_, Fig. 1. That the vibration directions of the two doubly refracted rays are in planes at right angles to each other, can be easily proved by using a nicol prism.[9] In most cases the separation of the two images is so slight as not to be perceived by the eye, and the practical method of testing a crystal section for double refraction will be given later, p. 27.

The crystals that show double refraction are further divided into two groups, _uniaxial_ and _biaxial_:

(1) ▄Uniaxial▄, or those in which the optical characters are symmetrical to _one_ direction, called an optic axis. This _optic axis_ is the crystallographic vertical axis, _ć_; and parallel to this direction there is a single value only for the light velocity and no double refraction takes place.[10] Hence any section parallel to the base (001) being at right angles to the optic axis, acts like a section of an isotropic crystal and transmits all the perpendicularly incident rays of light with no change. In any other section double refraction takes place and it can be proved by using a nicol prism that the two rays have ether vibrations, one in the plane passing through the incident ray and the _ć_ axis of the crystal, and the other in a plane at right angles thereto, hence in the basal plane. This latter ray, which has a constant velocity, is called the _ordinary ray O_; and the other ray, with velocity varying with the inclination of the section to _ć_, is called the _extraordinary ray E_.[11]

The vibration directions are either parallel or symmetrical to cleavage cracks and crystal outlines. In sections parallel to the optic axis, the two doubly refracted rays have the maximum difference in velocity of transmission, and hence their vibration directions are called _principal vibration directions_[12] and the plane containing them an _optical principal section_. In these sections the refractive index of the ray vibrating parallel to _ć_ (extraordinary ray) is denoted by ε, and that of the ray vibrating parallel to the basal plane (ordinary ray) by ω.[13]

To this group belong all _Tetragonal_ and _Hexagonal_ crystals.

(2) ▄Biaxial▄, or those in which the optical characters are no longer symmetrical to an optic axis but to three planes at right angles to each other (for monochromatic light). These crystals have, however (for light of each wave-length and for each temperature), _two_ directions parallel to which there is a single value only for the light velocity and hence no double refraction. These directions are called “_optic axes_.”[14] An investigation of these biaxial crystals shows that of all the rays traversing these crystals there are three rays which advance with maximum, minimum and some intermediate velocity. The vibration directions of these three rays are called the _principal vibration directions_ and are at right angles to each other (being the intersections of the three planes above referred to). The direction of ether vibration of the fastest ray is denoted by a, of the slowest ray by c, and of the ray advancing with intermediate velocity by b.[15] Each of the three planes, containing two principal vibration directions, is called an _optical principal section_. The index of refraction of the a ray is denoted by α, of the b ray by β, and of the c ray by γ.

To this group belong all crystals in the _Orthorhombic_, _Monoclinic_ and _Triclinic_ systems.

In the _Orthorhombic_ system, the principal vibration directions are parallel to the crystallographic axes; hence all pinacoidal sections contain two of these principal vibration directions. In all sections parallel to the three crystallographic axes _ă_, _ƃ_ and _ć_, the vibration directions are parallel or symmetrical to cleavage cracks, crystal edges, etc.

In the _Monoclinic_ system, one principal vibration direction is parallel to the ortho axis _ƃ_, the other principal vibration directions are in the plane of symmetry, at right angles to _ƃ_, but are not parallel with either the vertical axis _ć_ or the clino axis _á_. In clino pinacoid (010) sections the principal vibration directions will make definite angles with crystallographic lines, such as cleavages or crystal outlines. These angles are called _extinction angles_. They will vary, in this system, with reference to the direction of the _ć_ axis from a maximum on the clino pinacoid (010) to 0° on the ortho pinacoid (100), when the vibration directions of the two doubly refracted rays will be parallel and at right angles to the plane of symmetry. Hence the vibration directions are parallel or symmetrical to cleavages, edges, etc., _only_ in sections parallel to the ortho axis _ƃ_; but in all other sections are unsymmetrical.

In the _Triclinic_ system, the principal vibration directions are not parallel to the crystallographic axes, and there is no definite relation between these directions and the crystallographic axes; hence in all possible sections there will be extinction angles.

In all biaxial crystals the two _optic axes_ are inclined to each other, making what is called the _axial angle, 2V_, the apparent angle measured in air being _2E_. The optic axes lie in the plane, called the _axial plane_, which contains the principal vibration directions a and c. The axial angles are bisected by these principal vibration directions, the direction bisecting the acute angle being called the _acute bisectrix, Bx_{a}_, and that bisecting the obtuse angle the _obtuse bisectrix, Bx_{o}_. An approximate idea of the value of the axial angle can be obtained by the use of the petrographical microscope, as described later, p. 47. The axial angle is often a convenient distinction between such minerals as muscovite and biotite.

The axial angle will vary with the temperature and with light of different wave-length or color, and this variation is called _dispersion_ of the optic axes. Dispersion of the principal vibration directions also takes place in monoclinic and triclinic crystals, but can be usually disregarded.

In closing it is very important to remember that any section of an anisotropic crystal (not at right angles to an optic axis) will always transmit two rays of light with different velocities and with vibration directions in planes at right angles to each other. Isometric crystals, of course, produce no double refraction of light.