Hence, if a plate be cut from a crystal of Iceland spar perpendicular to the axis, all rays sent across this plate in the direction of the axis will produce but one image.  But, the moment we deviate from the parallelism with the axis, double refraction sets in.  If, therefore, a beam that has been rendered conical by a converging lens be sent through the spar so that the central ray of the cone passes along the axis, this ray only will escape double refraction.  Each of the others will be divided into an ordinary and an extraordinary ray, the one moving more slowly through the crystal than the other; the one, therefore, retarded with reference to the other.  Here, then, we have the conditions for interference, when the waves are reduced by the analyzer to a common plane.

Placing the plate of Iceland spar between the crossed Nicol prisms, and employing the conical beam, we have upon the screen a beautiful system of iris-rings surrounding the end of the optic axis, the circular bands of colour being intersected by a black cross (fig. 45).  The arms of this cross are parallel to the two directions of vibration in the polarizer and analyzer.  It is easy to see that those rays whose planes of vibration within the spar coincide with the plane of vibration of either prism, cannot get through both.  This complete interception produces the arms of the cross.

[Illustration:  Fig. 45.]

With monochromatic light the rings would be simply bright and black—­the bright rings occurring at those thicknesses of the spar which cause the rays to conspire; the black rings at those thicknesses which cause them to quench each other.  Turning the analyzer 90 deg. round, we obtain the complementary phenomena.  The black cross gives place to a bright one, and every dark ring is supplanted also by a bright one (fig. 46).  Here, as elsewhere, the different lengths of the light-waves give rise to iris-colours when white light is employed.

[Illustration:  Fig. 46.]

[Illustration:  Fig. 47.]

Besides the regular crystals which produce double refraction in no direction, and the uniaxal crystals which produce it in all directions but one, Brewster discovered that in a large class of crystals there are two directions in which double refraction does not take place.  These are called biaxal crystals.  When plates of these crystals, suitably cut, are placed between the polarizer and analyzer, the axes (A A’, fig. 47) are seen surrounded, not by circles, but by curves of another order and of a perfectly definite mathematical character.  Each band, as proved experimentally by Herschel, forms a lemniscata; but the experimental proof was here, as in numberless other cases, preceded by the deduction which showed that, according to the undulatory theory, the bands must possess this special character.

Sec. 10. Power of the Wave Theory.