CHAPTER XVI. OPTICAL PHENOMENA OF CRYSTALS IN CIRCULARLY POLARISED LIGHT. Modifications in Crystal Figures Produced by one Quarter-Wave PlateExplanation of the Phenomena-Results of Polarising and Analysing Circularly-Quartz in Circularly-Polarised. Light-Spiral Figures showing the Relation of Uni-axial and Bi-axial Axes. HAVING traced the general phenomena of crystals when examined in convergent plane-polarised light, we next proceed to examine the appearances they present in circularly-polarised light; being prepared by our previous experiments with this description of light for some interesting variations of the phenomena. 180. Effects of a Single Quarter-Wave Plate on the Rings of Crystals. We place first the large quarter-wave plate (in its usual position) in the ordinary slide-stage of the polariscope; and place the plate of calcite. cut across the axis in the crystal stage. The calcite loses its black cross, as we should expect, the cross being replaced by a thin (mere lines) nebulous grey cross which rotates with the analyser, on either side of the arms of which alternate quadrants of rings are dislocated as in C, Plate VII., the light. rings in one quadrant being opposite the dark parts in its neighbours. This figure does not change in the least as the analyser is rotated, but the quadrants and rectangular nebulous lines simply rotate with it. Bi-axial crystals give similar phenomena, the arms of the cross which pass through the axes being replaced by nebulous lines, on each side of which the semicircles of each system of rings are dislocated. This is most distinctly shown by placing in the crystal stage a plate cut across one axis only, as in the nearly circular rings of one axis in sugar-candy. If the quarter-wave plate be rotated 90°, the quadrants or semicircles which were first the smallest, will gradually become the largest, and vice versâ. Precisely similar effects will be found if the large quarter-wave plate be withdrawn, and the light analysed through the smaller one, placed in its usual position between the crystal and the analyser. 181. Explanation of the Phenomena.-This strange dislocation of the rings is easily explained, if we remember the original composition of the circularly-polarised ray, which is compounded (in passing through the mica-film) of two rectangular plane vibrations, one of which is a quarterundulation in phase behind the other-or in other words, referring to Fig. 171, one vibration in the middle of its swing acting upon another at the moment of rest, represented by the arrows in that figure. In the quarter-wave plate, sup. posing the plane of polarisation to be vertical, the vibrations are diagonal; and may be represented by the diagonal pairs of arrows in Fig. 187. Let this figure represent the plate of calcite with polariser and analyser crossed: in each quadrant the circularly-polarised ray, on entering the crystal, is doubly refracted into its plane-polarised components, one of which enters the plate a quarter-undulation behind the other. we have already seen (Fig. 180, § 160) that the crystal itself doubly-refracts any non-central ray into two rectangular components represented by radii and tangents to the circles; and in every uni-axial crystal, either the radii or the circles are But uniformly the most retarded—in the case of calcite the radii. Now in each order of colours or "ring," there is some position or distance from the centre where the retardation is either a half-wave or an odd multiple of a half-wave; and on the other hand, mere inspection of Fig. 187 shows that in the middle of each quadrant the two plane vibrations emerging from the mica-film (and after composition into a circular orbit, again decomposed) coincide with the plane vibrations-radius and tangent-in the plate of calcite. It is also seen that whereas in the calcite alone, all the radii are at given intervals retarded one or more half-waves behind their tangents, it is different with the mica retardations. In two quadrants the vibrations, A B, A B, coincide with radii, while in the alternate ones, a b, a b, coincide with tangents. All the uniform annular half-wave retardations of the calcite are therefore in two quadrants augmented by an additional quarter-wave retardation from the mica; and in the intermediate quadrants counteracted by a quarter-wave retardation of the opposite polarising plane. The result is therefore a dislocation by two quarters, or half a wave; which brings the bright rings of one against the dark rings of its neighbouring quarter. 182. Result of Polarising and Analysing Circularly. This having been demonstrated, place both quarter-wave plates in their usual positions, and the calcite in the crystal stage between them. Another very beautiful modification follows. With analyser crossed or parallel, all cross lines or dislocations have vanished, leaving only perfect circular coloured rings (D, Plate VII.). But as the analyser is rotated, alternate quadrants expand and contract in a beautiful manner, till at 45° we have the dislocated quadrants, and at 90° the complementary perfect rings to those in the first position; the successive appearances being represented in Fig. 188, A, B, C. The appearances in a bi-axial, such as nitre, are analogous and beautiful, all brushes having vanished, and each axis being surrounded by unbroken rings (E, Plate VII.). And lastly, at the point when the rings are perfect and unbroken, if either the crystal stage with all it bears-crystal, quarterwave plate, and analyser or even only the quarter-wave plate and analyser, be rotated, no change whatever occurs; the rings remain unbroken, and all trace of polarising planes, as theory |