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

M

FIGURE 2.-Diagram of apparatus to illustrate the principle of polarization by reflection discovered by

Malus in 1808.

M and N represent mirrors direction of the axis of the

adjustable with respect to the

apparatus and also rotatable about the axis.

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 of the rotation to thickness. The apparatus designed by Biot about 1814 for studying polarization in general is shown in figure 3. The 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.

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

T

FIGURE 3.-One form of Biot's original apparatus.

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

[a]=

100 X rotation
weight %Xdensity length

or

(100%) or 100€.

α

(12)

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

stance per 100 g of solution, and c is the grams per 100 ml of solution. It is the hypothetical rotation produced in unit length by 1 g of the active material dispersed in a volume of 1 ml, which in present day nomenclature, is termed "specific rotation." Molecular rotation is the hypothetical rotation produced in unit length by 1 gram-molecule of the active material dispersed in (or condensed into) a volume of 1 ml.

This work of Biot appears to have been the foundation of all polarimetry. From this time on, rapid strides were made in the improvement of apparatus, and there resulted the science of Polarimetry as we know it today. A few years later, the polarizing plate of black

FIGURE 4.-Original form of the nicol prism.

A, Diagrammatic sketch; B, detailed sketch of limiting rays (1 and 2) and of the various angles. DAC and BCA are right angles.

glass and the achromatized calcite analyzer rhomb had been replaced by the nicol [10] prism, previously mentioned, which was a far more effective and convenient device for polarizing light than the glass plate. It consisted of a rhomb of Iceland spar cut diagnonally and the two pieces cemented together in such a manner that one of the doubly refracted rays is reflected to one side, and the other passes on through the prism.

(b) TYPES OF POLARIZERS (FIG. 6) AND POLARISCOPES (FIG. 7)

The simple polariscope of Biot was improved by Mitscherlich [11] and by Ventzke [13], one of whom appears to have been the first to use two nicols, and by Robiquet [12] who added the Biquartz of Soleil [14], thus making the setting dependent upon the transition tint (tiente de passage), and many others. Some transition tint instruments are still in use.

In 1856 Pohl [15] attempted to increase the sensitivity of the simple polariscope by the use of a mica halfshade, but was not entirely

successful. However, his idea was later satisfactorily developed by Laurent [16]. In 1845 Soleil [14] had invented the quartz-wedge compensating system and added it to the polariscope, thus laying the basis for the modern saccharimeter.

In 1860 Reverend William Jellet [17] described the first satisfactory halfshade polariscope. The utilization of the halfshade principle was the first important step in the perfection of the modern instrument. Prior to this, with the exception of the Soleil biquartz transition tint plate, both the polarizing and analyzing devices were simple nicol prisms, the "end point" being determined by setting the instrument for a minimum of light intensity in the field. Jellet's contribution introduced into polariscope design the photometric field. To construct his halfshade device, which he used as the analyzer, he selected a rhomb of Iceland spar several times longer than its other dimensions, and squared off the end faces. He then sliced the resulting prism parallel to its long dimension, BS' and at a small angle, SCD, to the short diagonal D'D of the end faces (as indicated in fig. 6A), reversed the two pieces end for end, and cemented them together (fig. 6B). In this manner he obtained a compound prism (shown in cross section in fig. 6C) whose principal crystallographic section A'C in one half made a small angle to that (CA) in the other half, the principal crystallographic section of each half being equally inclined to the short diagonal of the end face. Diaphragms were placed centrally at each end of the prism. One ray (the ordinary ray O' and 0) came straight through, while the other (the extraordinary E' and E) was deviated slightly in each half and diaphragmed out. Thus the light in one half of the field was polarized in a plane making a small angle (about 2°) with the plane of polarization of the light in the other half of the field.

In 1870 Cornu [18] improved upon Jellet's idea by removing a wedgeshaped section from a nicol prism and recementing the two halves. Thus the plane of polarization in each half of the field made a small angle with that in the other half, as in Jellet's prism.

Schmidt and Haensch [19] simplified Cornu's prism by removing the wedge-shaped section from one half only of the nicol prism, the three pieces then being cemented together as before. In mounting, the divided half was placed toward the analyzer, and each part of this half gave light vibrating in a plane, which made an angle equal to the angle of the removed section, with the plane of vibration of the light coming from the other part. This angle is known as the halfshade angle. The field of the instrument thus appears divided into two parts, and the setting is made by turning the analyzing nicol until the parts become of equal intensity. The sensitivity of the instrument depends on the magnitude of the angle of the halfshade. As the angle diminishes, the precision with which a setting can be made increases. However, the total illumination of the field diminishes with the halfshade angle. An angle of about 2.5° is the minimum working value for ordinary conditions of measurement.

The advantage of the halfshade principle was universally recognized, and a number of halfshade polarizing systems were introduced by various investigators. Three of these, the Laurent, the Lippich, and the Jellet-Cornu as modified by Schmidt & Haensch, have been extensively used by polariscope builders.