This restoration of light which has been described in the case of Iceland spar is manifested by doubly refracting crystals in general, and forms a very simple and delicate test of the existence of double refraction, which may be applied when, from the feebleness of the doubly refracting power or the thinness of the crystalline plate, it would be difficult or impossible to make out a separation of the images. It may easily be observed by musing sulphate of limo or selenite, a common mineral, which has a very perfect cleavage in one direction.
But if the plate of selenito be very thin, not so thin however but that knell a plate may be readily obtained by cleavage, a new and splen did class of phenomena make their appearance, as was discovered by Arago. In those positions in which a thick plate simply restores a portion of the light, a thin Onto is seen arrayed in gorgeous colours, changing with every change of thickness, and varying too when the plate is considerably inclined. If the plate be fixed, and the analyzer be made to revolve, the colours change in a remarkable and when the rotation amounts to DO° the original colour at any point replaced by its complementary, so that the two superposed make white light. This law is found to hold good for any two azimuths of the analyzer separated by DO°, and not merely for the azimuths 0° and DO°.
It would pass the limits of this article to describe the phenomena of the colours of crystalline plates hi all their details, and the etill more curious and complicated coloured rings or curves seen about the optic axis, or the two optic axes, of uniaxal or biaxal crystals. Indeed the subject has been introduced in this place only to enable the reader to form a better idea of the evidence in favour of the view taken in the undulatory theory of the nature of polarization.
The laws of the phenomena of crystalline plates were most carefully investigated by M. Biot and Sir David Brewster, and to account for them the former imagined his theory of moveable polarization. Dr.
Young first showed that on the undulatory theory the retardation of one of the two oppositely polarized rays which passed through the crystalline plate relatively to the other was precisely that required to produce, by ordinary interference, the tint observed. Huygens's demonstration of the laws of reflection and refraction intimately con nects refraction with velocity of propagation, and thereby permits of the retardation in question being calculated from the observed pheno mena of double refraction, without making any assumption as to the nature of polarization. But it remained to be shown why no pheno
mena of interference should be perceived unless the light incident on the crystal were polarized, and the emergent light were subsequently analyzed.
It occurred to MM. Arago and Fresno] that it would bo interesting to examine in what manner the interference of two rays of light, which, as regards length of path, are in a condition to interfere, might modified by previous polarization of the rays. The memoir contain ng an account of this important investigation is published in the 10th volume (1819) of the Annales de Chimie,' p.288, and a full account of it is given in Sir John Herschel's Treatise on Light. The laws of inter ference of polarized light in truth might have been ebtained at once from the phenomena of the colours of crystalline plates by assuming those colours to be due to into ; but it was highly important at the time to establish them in a more direct manner, by the observation of what were incontestably fringes of interference. They may be thus briefly enunciated :—(1) Two rays of light coming from the same source, and polarized in rectangular planes, are incapable of inter fering. (2) Two rays coming from the same source, and polarized in the same direction, interfere exactly like rays of common light. (3) Two rays coming from the same source of common light, and polarized in rectangular planes, may be afterwards analyzed without acquiring thereby the property of. mutually influencing each other. (4) But two rap polarized in rectangular planes and after wards analyzed, do interfere, provided they come from the same source of polarized light. (5) In the phenomena of interference produced by rays which have experienced double refraction, the character of the interference is not determined simply by the difference of path ; it is necessary in certain cases to change this difference by a semi undulation. The half undulation must be added or not according as the planes of primitive polarization and of analyzation lie in alternate irs or in the same pair of opposite quadrants made by the rectan gular planes of polarization of the two polarized rays transmitted by the crystalline plate.