If light, polarized by the polarizer, be transmitted through thin doubly refracting crystals, and analyzed by the analyzer, splendid colours will become visible; and on rotating separately either the polarizer or the analyzer, at each quarter rotation the colours will change, being complementary to those at first visible, or such as are requisite with the first to make white light. We have seen (fig. 19) that white light consists of seven coloured rays, or of three primary colours—red, yellow, and blue, which, by superposition, form the others; and thus red is complementary to green, which consists of blue and yellow, the two sets of complementary colours appearing and vanishing as the light and darkness did when the crystals were not used.
These colours are produced by interference. The compound rays of white light (fig. 30 l) passing through the polarizer (t) are all polarized in one plane; the crystal (d) depolarizes this light, i. e. doubly refracts and resolves it into two sets of rays polarized in planes at right angles to each other, forming the ordinary, O, and the extraordinary ray, E. Each of these two sets of rays is resolved by the analyzer (s) into two other sets, polarized in planes at right angles to each other; so that in all there are four sets, two in one plane and two in the other; and, the primary rays of the two sets in each plane being in different stages or phases of undulation, in consequence of the retardation of the extraordinary rays, the undulations of certain coloured rays check and annihilate each other, while the remainder or complementary conspire and pursue their course, producing the appearance of colour, this effect being reversed at each quarter-revolution of the analyzer.
An idea of what is meant by phases of undulation may be obtained by reference to fig. 29, in which the undulations, a, b, are in similar states or phases, and so conspire in action, while the wave c is in a different phase and half an undulation behind the others; hence it would check or interfere with either of the other waves (a, b), the etherial molecules of the two, which vibrate perpendicularly or at right angles to the direction of the wave, acting to the same extent and in opposite directions.
In fig. 30 the analyzer is represented as composed of a natural crystal (rhomb) of calcareous spar, which transmits both sets of rays; but in the ordinary analyzer or Nicol’s prism—which is made by dividing a rhomb through the obtuse angles into two wedge-shaped pieces and cementing them together again with balsam, only one set of rays is transmitted at each quarter-revolution, the other being refracted out of the field. In the case of the tourmaline, one of the sets of rays is absorbed; so that the tourmaline, like the Nicol’s prism, is single-imaged.
Thus the colours produced by polarization are the same as those of the spectrum, but separated in a different way, both arising from the elementary coloured rays of the compound white light. For while the spectral rays are separated by dispersive refraction, the polarized coloured rays are separated by the interference and annihilation of some rays, the remainder passing on to produce the colours.
When the position of the depolarizing crystal is such that the plane of the polarized light coincides with the direction of the optic axis or axes, the light is not doubly refracted nor polarized in certain parts; hence these parts appear white if the plane of the polarizer and analyzer coincide, and black if they be crossed. A crystal cut at right angles to its optic axis, with its length directed towards the polarizer and analyzer, is in this position, and it exhibits alternately a black and white cross, with one or two sets of concentric rings of complementary colours at each quarter of a rotation.
To prepare crystals for examination by polarized light, a little Epsom salt, nitre, or borax should be dissolved in water, a drop placed upon a slide, and dried at a gentle heat. The crystals should then be mounted in balsam, and viewed as transparent objects.
To see the cross and rings, the crystals should be sawn or cut across transversely, the ends being polished on a strained piece of silk moistened with water, and the sections mounted in balsam.
The property of doubly refracting and polarizing light is not confined to crystalline substances, being also possessed by many organic bodies, for the details of which I must refer to the article Polarization in the ‘Micrographic Dictionary.