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and require the measurement of (the arctangent of the ratio (b'a') of the reflected components normal to and in the plane of incidence) and 28 (the phase difference introduced between the components on reflection). Moreover, it is assumed, as above, that the incident light is monochromatic and polarized in a plane having the azimuth Y1=/4= In consideration of relations (a), (b), and (e) of eq 9, these equations may also be written in terms of functions of the ratio of the axes of the reflected ellipse and the azimuth of its major axis. sin tan cos 24 cos 2y

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The coefficients, μe and Ke, determined experimentally at different angles of incidence, will vary with that angle. The relation between coefficients, Mo and for normal incidence to those for any other incidence may be simplified greatly by neglecting all squares of higher

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Ko,

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are adequate in computing the coefficients at normal incidence.

As in the reflection from transparent media, surface films are disturbing factors, and care must be taken to eliminate them as far as possible if the optical coefficients of metals are determined by this catoptric method. Under the best conditions, the method does not yield results with an accuracy comparing to that of results obtained by dioptric methods, but it can be used in cases where they are practically inapplicable.

9. SEGREGATION OF PLANE POLARIZED LIGHT BEAMS

(a) POLARIZERS FROM LARGE CRYSTALS

While a practically plane polarized beam of light is easily obtained by reflection from mirror surfaces on transparent media, the method is, as already stated, inefficient and unsuited for most polarimetric measurements. The resolution of natural light into two equally intense plane polarized beams by double refraction serves, on the contrary, as an ideal method of producing polarized light whenever it is possible to segregate one of the component beams without undue loss of intensity. In some cases this segregation is accomplished to a degree by the crystal itself. Tourmaline, for example, not only resolves natural light into plane polarized beams but also absorbs them

differentially. As a result, a plate of no great thickness (possibly 1 or 2 mm, depending on the crystal) transmits very little more than the extraordinary beam. The oscillation direction in the extraordinary beam lies in the plane containing both the normal to the plate surface and the optic axis. This plane, since it is normal to the face of the plate, is termed the principal section of the refracting surface. Obviously two such plates in series with their principal planes at right angles will almost completely absorb both components, since the extraordinary of the first becomes the ordinary beam of the second.

Polarizers of this sort are not efficient because the transmitted component is also reduced materially in its intensity. Moreover, the differential absorption varies with wave length, and when complete polarization is almost attained with a minimum loss of intensity for one color, the intensities of other colors may in comparison be greatly reduced or the polarization for other parts of the spectrum may be far from sufficient. Similar disadvantages are found in certain artificial polarizers.

Crystals such as quartz and calcite are highly transparent for both beams over a very great range of wave lengths. Consequently, the production of an efficient polarizer requires only the segregation of one of the polarized components by some artificial means which does not materially reduce the intensity of the component. The comparative frequency with which sufficiently large crystals of quartz and calcite are found has caused these materials to become very important adjuncts in all polarimetric work. The smaller divergence between the refractive indices of the component beams in quartz has limited the use of this material in the production of simple polarizers for visible light. However, the difference between the calcite indices is sufficient in some directions through the crystal to cause a comparatively large deviation of the ordinary and extraordinary beams. This large divergence makes it easy to segregate either of the plane polarized beams. In fact, such a beam of plane parallel light may be obtained with a cross-sectional diameter equal to one-tenth the crystal thickness simply by the proper use of diaphragms. Obviously, the procurement of beams having the cross section (or aperture) often required would necessitate the use of unduly large crystals. Consequently, Nicol took advantage of the differences between the refractive indices for the two beams to effect the total reflection of the ordinary beam at an interface formed by a cementing material with an intermediate index, and he thus devised a type of prism which greatly increases the aperture obtainable at the expense of a comparatively slight loss of intensity. Of the various modifications of this prism, some have so nearly the form of the original cleavage crystal that the direction of the optic axis, the principal plane (section) of the faces, and consequently, the direction of the oscillation may be determined approximately by simple inspection.

In a calcite cleavage rhombohedron, the X-direction is the optic axis and makes equal angles with the three edges at either of the two fully obtuse corners formed by the cleavage surfaces. These edges include three facial angles of about 101°55' at these corners, and the optic axis makes an angle of about 63°44′ and 45°23′ with each edge and face, respectively. When light is incident normally on a face, the ordinary ray (direction of the ordinary beam) passes directly through

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.

2 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 plates1⁄2 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

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