In this property also circularly polarized light agrees with common or unpolarized light, but differs from rectilinearly polarized light.

3. Analyzed by a doubly refracting prism of Iceland spar, a ray of circularly polarized light gives constantly two equal images, in whatever plane the principal section of the prism be placed. For, as I have already stated, a ray of circularly polarized light is the resultant of two rays placed at right angles and differing in their phase by a quarter undulation; and, therefore, it must give equal images by the doubly refracting prism, in the same way that common or unpolarized light does, for the difference of phases has nothing to do with this character.

In this respect circularly polarized light agrees with common or unpolarized light; but is distinguished from rectilinearly (plane) polarized light, which in certain positions (before specified) yields one image only.

4. By two total internal reflections in the interior of glass, at an angle of about 5440, circularly polarized light is converted into rectilinearly polarized light. Thus if light circularly polarized be incident on Fresnel's rhomb, it emerges rectilinearly polarized, and the position of the plane of polarization at emergence makes an angle of +45° or -45°, with the plane of reflection according as the incident light was right-handed or left-handed. This experiment may be readily understood from the explanation already given of the action of Fresnel's rhomb in converting rectilinearly polarized light into circularly polarized light (fig. 46, p. 88). In fact, the two experiments are the converse of each other; the light called incident in the one case, being termed emergent in the other, and vice versa.

In this character, circularly polarized light differs equally from both unpolarized and rectilinearly polarized lights. For by two reflections of this kind, common light suffers no obvious change; while rectilinearly polarized light, under the same circumstances, is converted into circularly polarized light, provided that the plane of reflection be at an azimuth of 45° to that of primitive polarization.

5. If a ray of circularly polarized light be transmitted through a thin film of a doubly refracting crystal, and the emergent light be analyzed by a doubly refracting prism, two rays of complementary colours are produced.

In this character, circularly polarized light is decidedly different to common or unpolarized light, which when submitted to the same examination presents no colour. Rectilinearly polarized light, however, agrees with the circular light in producing complementary tints; but they are not the same in the two cases; those produced by circular light differing from those of rectilinear

light by an exact quarter of a tint, either in excess or defect, as the case may be.

To illustrate these facts, place a film of selenite, of uniform thickness, in the polariscope, and observe the tint which it yields by rectilinearly polarized light. Then interpose, between the polarizing plate and the selenite film, a circularly polarizing apparatus (as Airy's mica plate, or Fresnel's rhomb), and the tint seen by the analyzer immediately changes.

If a plate of calcareous spar, cut to show the circular rings and cross by rectilinearly polarized light, be placed in the polariscope, and circularly polarized light be used, we observe a system of rings and a cross (fig. 53), but which are very different to those seen by rectilinearly polarized light.

FIG 53.

The rings are divided into quadrants by the cross, every other quadrant being similar, while the adjacent ones are dissimilar. The rings ll appear to be abruptly and absolutely dislocated, those in the two alternate quadrants being pushed outwards or from the centre, by of an order, and those of the intermediate quadrants being as it were pulled inwards by of an Rings and Cross of Calc order. Instead of a black cross, we have a Spar produced by circularly polarized light. luminous one, the intensity of its light being uniform, and about equal to the mean intensity. If the plane of incidence pass through 135° and 315°, the phenomena of adjacent quadrants are exactly interchanged. But the most important difference produced by circularly polarized light, is, that no alteration is made by turning the analyzing plate round the incident ray.

If a plate of a biaxial crystal, as of nitre, be examined by circularly polarized light, we observe the double system of rings, but the black cross disappears. Every alternate semicircle of rings presents the appearance of dislocation.

The origin of the tints produced by circularly polarized light, have been so clearly and concisely explained by Sir John Herschel, that I cannot do better than use his words:

"When," says this eminent philosopher, " a ray propagated by circular vibrations is incident on a crystallized lamina, it may be regarded as composed of two; one polarized in the plane of the principal section, the other at right angles to it, of equal intensity, and differing in phase by a quarter undulation. Each of these will be transmitted unaltered; and, therefore, at their emergence, and subsequent analysis, will comport themselves in respect of their interferences, just as would do the two portions of a ray primitively polarized in azimuth 45°, and divided into two by the double refraction of the lamina; provided that a quarter undulation be added to the phase of one of these latter rays. Now, such rays will produce, by the interference of their doubly refracted positions, the ordinary and extraordinary tints due to the interval of retardation within the crystallized lamina. Hence, in the

present case, the tints produced will be those due to that interval, plus or minus the quarter of an undulation added to, or subtracted from, the phase of one of the portions; and, consequently, will differ one-fourth of a tint in order from that which would arise from the use of a beam of ordinary polarized light, incident in azimuth 45° in the lamina."

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6. If a ray of circularly-polarized light be transmitted through a column of syrup or oil of turpentine, lemon, &c., and then analyzed, either by a Nichol's prism, or a doubly-refracting prism, no colour is produced. For the circular wave is propagated along the liquid without suffering subdivision, and, therefore, at its emergence, no colour can be produced by the analyzer. In this character circularly-polarized light agrees with common or unpolarized light; but differs from plane polarized light. Circularly-polarized light," says Fresnel, “ differs from plane polarized light in not sensibly developing colours in plates of quartz perpendicular to the axis." According to the wave hypothesis this ought to be the case; for "a ray propagated by circular vibrations, when incident on rock crystal in the direction of the axis, will (by hypothesis) be propagated along it by that elasticity which is due to the direction of its rotation, the wave then will enter the crystal without further subdivision, and there will be no difference of paths or interfering rays at its emergence; and, of course, no colours produced on analyzing by double refraction."

I confess, however, I have not been able precisely to verify this statement, though, I doubt not, my failure has arisen from some defect in the apparatus used to produce circular polarization. I have always found a very feeble tint of colour in the axis. As Mr. Airy has very accurately described the phenomena which I myself have repeatedly seen, I prefer quoting his words:

FIG. 54.

polarized light.

"If circularly-polarized light pass through the quartz, on applying the analyzing plate, instead of rings, there are seen two spirals mutually enwrapping each other [as in fig. 54.]. If the [Fresnel's] rhomb be placed in position 135°, the figure is turned through a quadrant. If the quartz be left-handed, the spirals are turned in the opposite direction. The central tint appears to be white. With the rhomb which I have commonly used (which is of plateglass, but with the angles given by Fresnel for crown-glass), there is at the centre an extremely dilute tint of pink: I think it likely that this arises from the error in the angles, as the intensity of the colour bears no proportion to that in other parts of the spiral."

If a plate of right-handed quartz be superposed on a plate of left-handed quartz of equal thickness, and examined by circularly-polarized light, the left-handed slice being nearer to the

polarizing plate, we observe, by means of the analyzer, four spirals (proceeding from a black cross in the centre) which cut a series of circles at every quadrant. At some distance from the centre the black brushes are seen. If the right-handed slice be nearer the polarizing plate, the spirals are turned in the opposite directions.

8. Mr. Earnshaw inferred, theoretically, from Fresnel's formulæ, that if right-handed circularly-polarized light be incident nearly perpendicularly upon a plane surface of glass, the reflected light will be left-handed circularly-polarized, and vice versa. The Rev. Professor Powell has subsequently verified experimentally Mr. Earnshaw's theoretical deduction.

Airy's analyzer for Circularly-Polarized Light.-I have already stated and described two kinds of circularly-polarized light; the one called right-handed, the other left-handed. To distinguish them, Mr. Airy contrived an analyzer which suppresses one and transmits the other. "It is well known," he observes," that if circularly-polarized light is incident on Fresnel's rhomb, it emerges plane-polarized, and the position of the plane of polarization at emergence makes an angle of +45°, or -45° with the plane of reflection, according as the incident light was righthanded or left-handed. Let the light emerging from the rhomb be received on an unsilvered glass at the polarizing angle, whose plane of reflection makes the angle +45° with that of the rhomb. Now it is plain that if the light incident on the rhomb was righthanded, it becomes plane-polarized in the plane of reflection of the glass, and, therefore, is wholly reflected; if it was lefthanded, it becomes plane-polarized in the plane perpendicular to the plane of reflection of the glass, and, therefore, is wholly suppressed." It is then obvious, that this combination of Fresnel's rhomb and on unsilvered glass at +45°, or -45°, would form an analyzer for circularly-polarized light. But as Fresnel's rhomb is inconvenient, on account of its length, Mr. Airy has substituted "a plate of mica of such a thickness that the ray polarized in the plane of one of its principal sections is retarded either 4th, ths, or ths of a wave (according to the convenience of splitting) more than that polarized in the plane of the other. The mica being attached to the unsilvered glass, so that its principal section makes an angle of 45° with the plane of reflection, an analyzer is produced, which answers the same purposes, in general, as that described above."

6. ON ELLIPTICAL POLARIZATION.

Time will permit to say a few words only respecting elliptically polarized light.

If two systems of waves of equal intensity, polarized rectangularly to each other, differ in their progress a fractional number ofundulation, the vibratory movements of the ethereal molecules will be neither rectilinear nor circular, but elliptical. The waves formed by such vibrations will be elliptical, and may be compared to an elliptical helix (that is, to a helix traced round an elliptical cylinder), right-handed or left-handed, as the case may be.

Powell's machine gives a very good idea of elliptical vibrations and elliptical waves.

The manner in which two rectangularly polarized waves interfere and produce elliptical waves, is shown by Wheatstone's apparatus.

There are several modes of effecting the elliptical polarization of light. If in the experiments with Fresnel's rhomb (see Circular Polarization) the planes of polarization and incidence be at any other angle than 45° the emergent ray will be elliptically polarized.

Airy's mode of producing circular polarization may be used to obtain elliptical light; but the mica plate, through which the ray is perpendicularly transmitted, must be placed at an azimuth between that which yields circularly polarized, and that which admits plane polarized light.

Compressed, or unannealed glass, also yields elliptically polarized light, under conditions which I have explained when describing Dove's method of circular polarization.

Quartz also produces elliptical polarization when the direction. of the incident ray is inclined to the axis.

By reflection from metallic surfaces light becomes elliptically polarized. The elliptical light reflected from silver is nearly circular, while that from galena is almost plane: that is, the ellipsis in the one case is nearly a circle, in the other nearly a straight line.

Elliptically polarized light is not distinguishable, by the eye, from other kinds of light. If it be analyzed by a Nichol's prism, an unsilvered glass mirror, or a plate of tourmaline, it never vanishes during the revolution of the analyzer. By this it may be known from rectilinearly polarized light. But at different azimuths of the analyzer the intensity of the light varies; and by this it may be known from both unpolarized and circularly polarized light. If it be analyzed by a rhombohedron of calc spar, it gives two images in all positions of the analyzer. In this respect it differs from plane polarized light. But one of the images exhibits a defalcation of light, showing that the incident light is not common or unpolarized. If elliptically polarized light be transmitted through an uniaxial crystal (as