The optical properties of a uniaxial crystal are best understood by considering the shape of the Ray Surface, which consists of two shells with a common centre. One is a sphere, the other an ellipsoid of revolution, each passing through points on the rays determined by the velocities of transmission.
Evidently for every direction except that of the optic axis two rays are transmitted, an ordinary, with a velocity indicated by the sphere radius, and an extraordinary, with a velocity indicated by the corresponding radius vector of the ellipsoid, and the greatest differ If the vibration directions of the fastest and slowest ray are denoted by X and Z respec tively and a direction at right angles to these by Y, the shape of the ray surface may be judged from the shape of the principal sec tions XY, XZ and YZ.
once of velocity exists for the direction of transmission at right angles to the optic axis.
The spherical shell may surround the ellip soid shell or vice-versa. The former combi nation is called a positive ray surface (Fig. 1), the latter a negative (Fig. 2).
The Optically Anisotropic Biaxial Crystals. In all orthorhombic, monoclinic and triclinic crystals, the optical behavior varies with the direction, and while there are no true optical axes, there are, for monochromatic light and constant temperature, two directions of single refraction which are called optic axes from analogy with the direction of single refraction in the uniaxial crystals.
The ray surface consists of two intersecting shells symmetrical only to three lines at right The section XY (Fig. 3) cuts the two shells of the ray surface as a circle within an ellipse with radius, major and minor axes respectively slowest, fastest and intermediate velocities, while the section YZ (Fig. 4) cuts the two shells of the ray surface as an ellipse within a circle with radius, major and minor axes re spectively fastest, intermediate and slowest velocities.
The section XZ, the plane of the optic axes, cuts from the ray surface an ellipse and a circle which intersects the ellipse in four symmetri cally placed points, E (Fig. 5). The radius, major and minor axes are respectively the intermediate, fastest and slowest velocities.
angles and to three planes each through two of these lines. Two of the three lines are the vibration directions of the fastest ray and the slowest ray. It may be noted that when planes or axes of geometric symmetry exist they co made with planes or axes of optical symmetry.
Near but not at the points E common tan gent planes can be drawn to each shell. The directions, AA, normal to these common tan gent planes are directions of single refraction, the so-called optic axes. The acute angle be tween these is called the optic axial angle.
As in the uniaxial ray surfaces there are two types, the described sections being those of a positive ray surface with Z bisecting the acute angle between the optic axes; when X bisects this angle the ray surface is said to be negative.
Determining the Optical Properties of Crystals. The Light Used.— In general the light used is polarized, as the effects of the crystalline structure upon this are more readily studied. Some of the tests also require the use of monochromatic light, that is of light of one definite wave length, while other tests are made with white light.
Obtaining the Polarized Light.— Although occasionallyproduced by reflection of common light at a definite angle, or by double refraction and absorption, as in. the sim ple polariscope, known as the tourmaline pincers, the usual method is by sending common light through one of the vari ous forms of 'anicols') prisms, the original form of which de scribed by Prof. William Nicol was constructed as follows: A cleavage prism of transpar ent calcite (Fig. 6) is cut di agonally along the line H H and then the two parts are ce mented together with Canada balsam. The end faces are ground off slightly so that an angle of 68 degrees is formed. (See Fig. 6). The ordinary ray o with an index of refrac tion of 1.66 is totally reflected. The extraordi nary ray e with an index of refraction of 1.54 (practically that of the balsam) passes through the prism with little, if any, change. The plane of vibration of the nicol is assumed to be through the shorter diagonal.