(c) ELLIPTIC COMPENSATORS

Various kinds of elliptic compensators have been used but, in general, these may be divided into two classes-variable- and constantorder compensators. (The order of a compensator or halfshade is the relative retardation it produces, expressed in wave lengths.) Wellknown examples of the first type are the Babinet and strain compensators. It seems that the first of these was designed by Babinet merely to detect elliptically polarized light and was later adapted by Jamin for use in actual measurement. A more or less detailed description of this compensator can be found in most texts on physical optics, and an excellent example of its use is found in Drude's Investigation of the Optical Constants of Metals [14, 15].

With the original form of Babinet compensator, the use of an elliptic halfshade is not feasible because the field of view presents a series of bright and dark bands, which are indicative of the compensator order in the different parts of the beam and which are shifted when the ellipticity of the light is changed. With the Soleil modification it is, however, possible to use an elliptic halfshade because, in effect, each band is so broad that it covers the whole field, which therefore presents a practically uniform intensity.

The strain compensator also presents a field of uniform intensity and is often used in conjunction with an elliptic halfshade. Such a compensator consists of a plate of glass (or other suitable transparent isotropic material) which is so mounted that it may be subjected to positive and negative compressions in a direction perpendicular to the light beam and in the desired azimuth. Within reasonable limits, the relative retardation of such a compensator is proportional to the compression.

The quarter-wave plate (Senarmont's compensator) and the Brace elliptic compensators, which have much smaller orders, are examples of fixed-order compensators. These are both adapted to use with elliptic halfshades. In fact, high precision of measurement with any uniformfield compensator depends on such use. With such combinations a sensitivity has been claimed which permits, under best conditions, the detection of a change in axis ratio equal to 0.0001.

(d) FUNCTIONS OF ELLIPTIC COMPENSATORS AND HALFSHADES

The usual function of a compensator is to restore elliptical polarization to plane polarization. A quarter-wave plate compensator or its equivalent is obviously capable of so reducing any elliptical polarization, simply by making either the fast or slow axis of the compensator to coincide with the major axis of the light oscillation. The positions of the compensator axes in such complementary settings yield the data required to determine y for the major axis. Moreover, the azimuths of the oscillation planes of the resultant plane polarized beams, corresponding to the two complementary settings, may be determined by the analyzer nicol and the major axis bisects the acute angle between these planes. This acute angle is, therefore, equal to 24.

If the order of the compensator is less than a quarter wave, it will reduce elliptical oscillations to plane polarized light only when 2¥ Z2dc, the order of the compensator expressed as angular retardation. eq 9a, where, if d is replaced by de, it is evident that the maximum for a given 8, is reached when 4/4 or 3/4 and, therefore, when sin 28, sin 2¥).

As with the quarter-wave plate, there are complementary settings of the compensator, each of which results in plane polarized light and yields its own particular nicol setting. The Stokes method [16] uses these four settings (two of the compensator, C, and C2, and two of the nicol, N1 and N2) for determining not only y and y but also 28c, if the compensator is uncalibrated.

With the nicol and compensator only, it is impossible to determine when the latter has fully reduced (or compensated) the elliptical polarization. The function of a balanced elliptic halfshade is to indicate by a matched field when this compensation is complete. That of the unbalanced halfshade is similar, except that it indicates when the axis ratio of the oscillation leaving the compensator has reached a small definite value. As in ordinary polarimeters, the function of the nicol halfshade is to increase the precision of settings on the major axis of the plane (or the practically plane) polarized light emerging from the compensator.

Three different designs of the apparatus for determining C1, C2, N1, and N2 are possible. That is, the nicol and compensator may be borne on circles or verniers that rotate independently, a rotating circle which carries the nicol and also a rotating vernier for bearing the compensator, or the relation of nicol and compensator to circle and vernier may be reversed. This last design was that used by Stokes. Conse(C1+C2) quently, according to his method, -T/4 gave the reading which would make the axes of the compensator and ellipse coincide. Moreover, if C2-C1=c and N-N1=n are written, and if a balanced

tan n
tan c

2

and cos 24=

sin n

sin c

If an un

halfshade is used, then cos 28,= balanced halfshade is used, these formulas must be modified. The modified forms have been developed by Tuckerman [17] and by Skinner [13].

12. REFERENCES

[1] P. Drude, Theory of Optics, English ed. (Longmans, Green and Co., London, 1902).

[2] E. Edser, Light for Students (The Macmillan Co., New York, N. Y., 1927). [3] T. Preston, Theory of Light, 3d ed. (The Macmillan Co., New York, N. Y., 1901).

[4] A. Schuster, Theory of Optics (Edward Arnold, London, 1904).

[5] R. W. Wood, Physical Optics, 3d ed. (The Macmillan Co., New York, N. Y., 1934).

[6] N. H. Winchell and A. N. Winchell, Optical Mineralogy (D. Van Nostrand Co., Inc., New York, N. Y., 1909).

[7] W. B. Herapath, Phil. Mag. [4] 6, 346 (1853); 7, 352 (1853).

[8] M. Grabau, The Optical Properties of Polaroid for Visible Light, J. Opt. Soc. Am. 27, 420 (1937).

[9] J. C. M'Connel, Phil. Mag. [5] 19, 317 (1885).

[10] R. M. Emberson, J. Opt. Soc. Am. 26, 443 (1936).

[11] J. R. Collins, Rev. Sci. Instr. 9, 81 (1938).

[12] D. B. Brace, Phys. Rev. 18, 70 (1904).

[13] C. A. Skinner, J. Opt. Soc. Am. & Rev. Sci. Instr. 10, 491 (1925).

[14] P. Drude, Ann. Phys. Chem. [3] 34, 489 (1888).

[15] P. Drude, Ann. Phys. Chem. [3] 39, 481 (1890).

[16] G. G. Stokes, Phil. Mag. [4] 2, 420 (1851).

[17] L. B. Tuckerman, University Studies of University of Nebraska 9, 157 (1909)

III. MEASUREMENT OF ROTATION IN CIRCULAR

DEGREES

1. POLARISCOPES WITH CIRCULAR SCALES

(a) HISTORY OF DEVELOPMENT

About the year 1669 Bartholinus [1] discovered the double refraction in Iceland spar. A few years later the polarization of light was first noticed by Huygens [2] while repeating Bartholinus' experiments, but the phenomenon remained an isolated fact in science for more than a century afterwards. In the period 1766 to 1777 M. l'Abbé Alexis Marie Rochon [3], using doubly refracting prisms, perfected a device for measuring small angles with a precision 0.1 of 1 second. With this apparatus, constructed of rock crystal, he measured small angles, such as that subtended by the diameter of a planet, and with a similar one constructed of Iceland spar, he measured the diameter of the sun. His device consisted of a prism cut from a doubly refracting crystal in a direction to give maximum separation to the two rays. In addition to producing an angular separation of the two rays, the prismatic effect spread each of the rays into its spectrum. This latter being undesirable, Rochon added another equal glass prism in reverse position to achromatize the prism. He thus obtained un

FIGURE 1.-Rochon's double-image prism, indicating diagrammatically how the extraordinary ray diverges when the prism is constructed of calcite, A, and of quartz or rock crystal, B.

colored images and still retained the angular deviation between the two differently refracted rays.

He later found that more nearly perfect achromatism was obtained if the second prism was made of the same material as the first but cut in such a direction that the light passed through it along the optic axis, i.e., the direction of no double refraction.

In one form of Rochon's micrometer, this acromatized prism was placed in the tube of his telescope in such a manner that it could be moved back and forth along the axis of the telescope. The telescope was sighted upon the object to be measured and the two images brought just into contact by movement of the prism along the telescope axis. The constants of the prism and its position in the telescope gave the value of the angle being measured.

Rochon appears to make no mention of the fact that the two rays produced by his prism are polarized. It is probable that he knew this to be true but was not particularly interested in that fact. He was an astronomer and navigator and used his device for astronomical and nautical measuring instruments. However, before he

died in 1817, Rochon had the satisfaction of seeing his device used with great success by a young confrère named Arago, for an entirely different purpose, for the study of polarized light.

About 1808 Malus [4] discovered, accidentally, that light when reflected from the surface of glass, acquires properties similar to those possessed by light transmitted through a plate of a doubly refracting crystal, i.e., it is not the same in all directions around the line along which the ray is traveling, but appears to be two-sided, or "polar"; hence the term "polarization."

N

Malus in 1808.

M

M and N represent mirrors

This "two-sideness" of light may be detected by allowing it to fall upon another plane glass plate set at a proper angle. By maintaining the plate at the polarizing angle and rotating it around the beam, the reflected light is seen to vary in intensity as the plate is rotated, and in one position of the plate the reflected light vanishes altogether.

Arago [5], in 1810, discovered the rotation of the plane of polarization of polarized light. He noticed that when quartz, cut perpendicular to the optic axis, was placed between the two inclined plates, the position at which the light vanished was different from that when nothing was between the plates. Arago used Rochon's achromatized doubly refracting prism to good advantage in his studies on polarized light. The glass plate of Malus served as a polarizer, while Rochon's prism served as the analyzer, not only for Arago but later also for Biot. Biot might well be called the father of polarimetry, since it was he who worked out the fundamental physical laws upon which modern polarimetry is based.

Biot [6], in 1812, discovered the proportionality FIGURE 2.-Diagram of apparatus to illus- of the rotation to thickness. The apparatus trate the principle of designed by Biot about 1814 for studying polaripolarization by re- zation in general is shown in figure 3. The flection discovered by polarizer, M, was a black mirror set at the polarizing angle and whose mounting, B, could be rotated about the axis of the tube, T. B', which could also be rotated about the axis of the tube, T, carried the mounting, C, upon which the sample being studied was placed so that it could be turned in any direction. The light from white clouds of the sky was observed through the analyzer which consisted of an achromatized double-image rhomb of calcite (Rochon prism) mounted upon a divided circle.

adjustable with respect to the direction of the axis of the apparatus and also rotatable about the axis.

This prism, in general, produced two beams, one of which being undeflected was used, while the other, being deviated by an amount depending upon the angle of the doubly refracting prism, was disregarded. This probably was the forerunner of the nicol prism, since it seems only another step to make the separation of the two rays so great that one would be entirely lost from the field of view. In fact,

when the nicol prism was invented in 1828, its inventor described it under the title, "A method of so far increasing the divergence of the 2 rays in calcareous spar that only one image may be seen at a time." For studying the rotation of the plane of polarization in liquids, Biot replaced the tube, T, by supports to carry a tube closed with glass end-plates in which the liquid was placed. His original apparatus was described in 1811-17 [6, 7, 8]. In 1840 he described [9] certain modifications of his more general instrument, together with explicit precautions in using it for measuring the rotation of optically active liquids.

During the period 1815-40 Biot formulated practically all the fundamental laws of polarimetry in use today. He recognized the

difference between rotation produced by crystalline structure and that produced by substances when they appeared to have no crystalline structure, i. e., liquids and dissolved substances. The latter he believed to be due to the molecules themselves. He also recognized that each different kind of optically active molecule had a different or characteristic rotatory power. This, within the limits of his experiments, he found to remain the same regardless of whether the substance was in the solid, liquid, or vapor state. In order to have a comparable basis for the purpose of comparing the rotatory power of different kinds of molecules, he calculated from the observed rotation of each substance the rotation for unit length and unit density. This he called "molecular rotation" or "molecular rotatory power" because it had to do with the molecule rather than crystal structure, and he represented it by the symbol [a]. By his definition of [a] for the case of pure substances, [a]=a/density length or using present-day symbols, a/pl.

In the case of solid substances dissolved in inert liquids, he defined [a] as

In these equations, a is the observed rotation in circular degrees, p the density, the length in decimeters, p the grams of dissolved sub