the rhomb, as in the case of an isotropic plate; but the extraordinary ray, although deflected, is so directed that a plane containing both rays parallels the optic axis. This plane is the principal optic plane (or section) of the transmitting faces. The principal section for the artificial faces of a nicol prism are similarly determined, and the oscillation directions of the extraordinary and ordinary beams lie, respectively, in and perpendicular to it.

(b) POLAROID

Polaroid, which is a polarizing material in sheet form, consists of submicroscopic needle or thread-like pleochroic crystals of herapathite [7]2 (iodoquinine) embedded in a suitable matrix, such as cellulose nitrate or acetate, and all oriented in the same direction. It may be produced in almost any size desired. According to the patent specifications (U. S. Patent 1,951,664), it may be made in the following

manner:

Quinine bisulfate (1.5 g) is dissolved in 50 ml of methyl alcohol, brought to a boil, and stirred while adding 0.525 g of iodine as a 20percent solution in alcohol. Stirring is continued while a jell forms and until the mass has cooled. The herapathite is rapidly precipitated out of the solution as a jelly of interwoven submicroscopic needles. This jelly is then incorporated in a viscous suspending medium, such as a solution of cellulose nitrate or acetate dissolved in amyl or butyl acetate or other suitable solvent, and stirred until uniformly dispersed throughout. By pouring or flowing a viscous medium of this character, the mechanical forces acting upon the crystals are such that the crystals all turn until their long axis is substantially parallel to the direction of flow. The flowing in some cases is accomplished by extrusion through a long thin die (U. S. Patent 1,989,371) or by flowing past an edge (U. S. Patent 2,041,138). In either case, a flat ribbonlike sheet is obtained, having the crystals all oriented in the same direction. The crystals then behave approximately as a single large crystal the full size of the sheet. The active layer is protected by exterior layers of the cellulosic material or by glass plates.

In the central part of the visible spectrum, the polarization is about 99.8 percent complete, but at the ends of the spectrum, both in the extreme violet and in the extreme red, the polarization is not nearly so good [8]. This results in a faint residual purplish tint in the field instead of blackness when two pieces of Polaroid are accurately crossed, when using an intense white-light source.

In certain applications of polarized light, Polaroid is the equal of the nicol prism and in some cases is superior. It has opened up new fields of application to which the nicol prism is not adaptable.

For one class of work, however, at least in the present state of the art, the nicol prism still has no serious rival, namely in those applications where nearly complete extinction is required, as in precision polarimetric measurements. Here complete polarization is required, and any unpolarized light seriously interferes with the precision of the measurement.

This substance was named in honor of its discoverer, William Herapath, who studied this material from the standpoint of making polarizing apparatus from it. He was able to obtain single-crystal polarizing plates 1⁄2 inch or more square, which he believed would soon entirely supersede the nicol prism and the tourmaline plates then in use (1852) as polarizing media.

For most applications where a bright field or an interference pattern is used, Polaroid is optically as good as a nicol prism and has the advantages of being very thin and not being limited to a comparatively small free aperture, as is the nicol. Instead of displacing the nicol prism, Polaroid finds its most useful and satisfactory applications in those very cases for which the ordinary polarizing prism is least satisfactory or is inadequate. The two polarizing mediums are thus supplementary to each other.

Polaroid is finding use in strain detectors and analyzers, in threedimensional moving pictures, in removing glare for photographic purposes, and in education. Laminated spectacle lenses containing a film of Polaroid are being used in sun glasses for use both on land and on water, the Polaroid removing glare to a large extent. Being comparatively cheap and rather startling in some of the effects that may be produced, it is serving to arouse public interest in the phenomena of polarized light and its many uses in everyday life.

(c) METHODS OF LOCATING THE PLANE OF POLARIZATION

The extraordinary beam is transmitted by practically all modifications of the nicol; but even so, it is in many cases relatively difficult to determine the position of the principal plane, especially if there is some doubt concerning the type of the nicol in question. In such cases, the approximate direction of the oscillation is easily determined by using a plate of glass as a reflecting polarizer and the nicol as the analyzer to extinguish the light thus polarized. That is, the direction of oscillation in any light that would be transmitted by the prism lies in the prism section which coincides with the plane of incidence to the reflector when the nicol is set to extinguish the plane polarized reflected light, and that section is the principal section of the nicol if it transmits the extraordinary beam.

Under the very best of conditions, it is possible to set a simple nicol with a very satisfactory precision in the position for the extinction of plane polarized light. These conditions are, however, seldom realized in the performance of polarimetric measurements. Consequently, in order to increase the precision of the setting, the simple nicol has been so modified (or used in combination with a half nicol) that two half-fields rather than a practically uniform field appear. In many cases, these modifications (described elsewhere in detail) may be used either as polarizer or analyzer, although their use as polarizers is, with certain exceptions, considered preferable, and even necessary, in some polarimetric instruments. As polarizers these special "halfshade nicols" produce, in effect, two parallel and almost equally intense beams of plane polarized light with their oscillation directions mutually inclined at a small angle. In making observations, the simple analyzing nicol, instead of being set for extinction, is so adjusted that its polarizing plane divides this very acute angle between the oscillation planes of the two parts of the polarizer and at the same time makes the corresponding half-fields appear equally intense. If the beams from the polarizer are equally intense, the polarizing plane of the analyzer bisects the angle between their oscillation directions for a matched setting.

Many of the generally used types of halfshade nicols, and especially those composed of a full and half nicol, do not yield the

equality of intensity required to cause this bisection of the halfshade angle at match to an exactitude that is within the precision of a setting on matched fields. That is, the polarization plane of the analyzer set for match always lies closer to the oscillation direction of the beam with the more intense maximum than it does to that of the beam with the less intense. The magnitude of this deviation from actual bisection is precisely determined with difficulty, and there is consequently always some uncertainty concerning the actual positions (azimuths) of the oscillation directions of the two beams from a halfshade polarizer with respect to any chosen reference plane. Fortunately, in simple polarimetry, which is concerned chiefly with rotations of the plane of polarization, this uncertainty has no significance. In other cases, especially if they involve elliptically polarized light, it may be so troublesome that it is necessary to use a type of halfshade nicol that transmits two beams of the same intensity. Even then it is advisable to use the halfshade as the analyzer and the simple nicol as the polarizer, since it is obvious that the analysis of the elliptical polarization produced by any agent of unknown characteristics will be simpler if that agent acts only on a single uniformly plane polarized beam of light with a definitely known azimuth. In general, however, the use of a "halfshade" as an analyzer makes it more difficult to produce the necessary sharpness of division between the half-fields.

In measurements on elliptically polarized light, it is usually not only necessary to know at all times the precise relative angular position of the principal plane of the polarizer with respect to the bisector of the angle between the principal planes of the analyzer, but it is also necessary to determine with great precision its angular position with respect to other directions or planes, such as the direction of lines of electric or magnetic force, the planes of incidence of mirrors, or the principal planes of crystalline plates that are being tested or used as auxiliaries. For this reason it is always desirable, and sometimes necessary, to mount not only the analyzer but also the polarizer in circles that are so constructed and graduated that the nicols may be rotated through 360° and that any rotations may be measured to 0.01° or less. When such circles are a part of a combined polarimeter and spectrometer, some of the methods which have been used for determining the azimuth of the principal plane of the polarizer with respect to some reference direction in the instrument are easily employed.

In the M'Connel method [9] for setting the polarizer at a known azimuth, it is well to remove the polarizer temporarily from the collimator circle, since that nicol and the glass prism or plate (used in alining the axes of telescope and collimator perpendicular to the vertical axis of the polarimetric spectrometer by the Gauss eyepiece method), together with its supporting table, are replaced by an auxiliary nicol prism mounted in a suitable holder that fits the table mounting. This auxiliary nicol with its axis and the common axis of telescope and collimator alined is set so that its principal plane (approximately located as described above) makes a small angle with the vertical axis. The halfshade analyzer (its telescope at this stage being focused on the halfshade field and not as in the alinement tests for parallel light coming from the collimator) is then set for a match on the plane

polarized light being transmitted from the collimator by the auxiliary polarizer. After obtaining this setting, the circle of the prism table is rotated through 180°, so that the auxiliary nicol is reversed end for end, and a new setting of the analyzer is made. It is clear that the difference between the settings taken before and after the reversal is double the small deviation of the principal plane of the polarizer from the vertical axis. Consequently, a setting midway between these settings will yield a match on plane polarized light only when the principal plane of the polarizer contains the vertical axis. The auxiliary nicol is therefore removed and the collimator polarizer is replaced in its circle and rotated until the match for that setting of the analyzer is accomplished. This gives the polarizer setting on its circle for zero azimuth of its principal plane, and with this setting known, any other desired azimuth can be obtained to the degree of precision afforded by the sensitivity of the halfshade system and the analyzer and polarizer circles.

Polarization by reflection at the polarizing angle of incidence from specular surfaces on transparent materials has also been used [10, 11] to determine the position of the polarizer for zero azimuth. When the reflecting surface of the glass alining prism or its equivalent contains the vertical axis and its polarizing angle of incidence is known, the setting of the analyzer corresponding to zero azimuth of polarizer is easily obtained by an analyzer match on light reflected at that incidence. For this test the incident monochromatic light may be either polarized or natural; but if it is plane polarized, the azimuth of the principal plane of the collimator nicol with respect to the plane of incidence must not be too small, since the intensity of the reflected light will then be so low that a match setting of the analyzer is impossible.

When the polarizing angle of the reflector is unknown, it, and also the zero azimuth, may be determined with a precision approximating that of procuring an analyzer match if a series of observations is made for two or more azimuths of the polarizing nicol and at two or more angles of incidence for each azimuth. The azimuths (not exactly known) of the polarizer's oscillation plane with respect to the plane of incidence should be equally distributed above and below zero but not so near that observations are difficult. The angles of incidence should be chosen in about equal numbers on each side of the only approximately known polarizing angle and should not depart from it by more than a few degrees except in preliminary observations. When the observations (angles of incidence and analyzer settings for match) are plotted, the curves (almost straight lines for a narrow range near polarizing incidence) will intersect at the polarizing angle, and the analyzer reading corresponding to this incidence is the analyzer setting for matching on light polarized in the plane of incidence.

Although a graduated collimator circle for the polarizer is advantageous, it is obvious that none of these methods require this, since all necessary azimuth readings may be referred to the analyzer circle. Moreover, once the analyzer setting for light polarized in the plane of incidence is obtained, the polarizing spectrometer may be moved about and used to set the principal plane of polarizers in other instruments with respect to vertical, provided the spectrometer is supplied with adequate leveling devices, which assure a coincidence of its axis with that direction.

10. PRODUCTION OF ELLIPTICALLY POLARIZED LIGHT

(a) BY DOUBLY REFRACTING PLATES

Doubly refracting plates for the production and compensation of elliptically polarized light can be prepared from either uni- or bi-axial crystals. Strained plates of isotropic materials, since they show the so-called "accidental double refraction," are also often used in polarimetric instruments instead of crystalline plates.

Doubly refracting plates from uniaxial crystals are usually cut parallel to the optic axis. Consequently, a beam of plane polarized light normally incident on such a plate is, in general, resolved into two undiverging plane polarized components, the extraordinary with its oscillation plane parallel to the optic axis (X- or Z-axis, depending upon whether the crystal is optically prolate or oblate) and the ordinary with its oscillation plane parallel to the optic normal.

If the plate is from an optically oblate crystal, the extraordinary component traverses it with the greater velocity, Heo. If by convention the direction of the faster oscillation is chosen as the reference direction in the plate, the optic axis (X-axis), parallel to that direction in this case, should for convenience be marked "fast." In the case of plates from optically prolate crystals, .. and the optic axis (Z-axis) is the direction of the slower oscillation and should be marked "slow."

If the amplitude of the incident rectilinear oscillation is "a", and its azimuth with respect to the fast axis of the plate is Ypi the amplitudes of the components in, and perpendicular to, that axis are a cos y, and a sin y, at incidence. Neglecting loss by absorption and reflection, the amplitudes are unchanged on emergence from the plate, but a phase difference proportional to the plate thickness, D, will have been introduced between the oscillations, which were obviously in phase at incidence. According to eq 3, and since z=D, this phase difference, d=2πD(μ。—μe)/λ=dD (in an optically oblate plate, for example), and in eq 5 to 9, it is the equivalent of 28. Moreover, according to identities of the preceding eq 8, the ratio of the amplitudes a sin la cos y=tan y=tan . When 8, and are known, the characteristics of the resultant elliptical oscillation may be determined from eq 9.

To determine 8, with the needed accuracy usually requires some precise method of calibration, but its approximate value can be computed from D and the refractive indices if the crystal and the manner in which it was sectioned to produce the plate are known. Moreover, since the difference between the indices increases in gencral with decreasing wave length, it is usually necessary to determine 8, at several points in that portion of the spectrum in which the plate is to be used.

Such doubly refracting plates are used chiefly as accessories for polarizing microscopes and for such polarimeters as are used in measurements on elliptically polarized light. These accessory plates are usually rated in terms of the phase difference (or relative retardation) which they introduce between components having some designated wave length.

Although the relative retardation, especially when small, is more commonly expressed in circular degrees (or possible radians), the equivalent number (N) of wave lengths may also be used to designate