CRYSTALS OF TWO AXES. 



139 





/ 



The rings seen ii\ ciystals cut across tlie 

 axis, wlien examined in cii'cularly polarized 

 light, exhibit some singular peculiarities. 

 They are divided into quadrants by a cross 

 which is neither very daik nor very biig^t, 

 and which does not change in intensity witli 

 the revolution of the analyzer, but turns with 

 it. The rings in the alternate quadrants are 

 vncovformahle, those in one opposite pair 

 being nearer to the centre, and those in the 

 other more distant from the centre, by a 

 quarter of an interval, than the corresponding 

 rings in plane polarized light. This singular 

 arrangement is shown in Fig. 22. 



Mr. Airy found that light may be circu- 

 larly polarized by refraction, in passing 

 through laminte of crystals which doubly refract ; provided the thickness of the 

 laminai used is such as, ou the undulatory theory of light, is just sufficient to 

 effect a. retardation of one of the rays produced by the double refraction, one- 

 quarter of an undulation behind the other, or to advance it one- quarter of an 

 undulation before the (ither. The mineral employed by him for this purpose, 

 and which is more conveniently prepared of suitable thickness than most others, 

 is mica ; of which the laminae are easily separable, and cleave in large sheets 

 without breaking. A lamina reduced to a thickness proper to produce circular 

 polarization is commonly called a " quarter-wave lamina." 



For some time after the discoveries had been made of which a brief account 

 has here been given, it was supposed that all doubly refracting crystals have 

 but a single optic axis. In the year 1817, however. Sir David Brewster 

 announced the remarkable fact that most crystals have two optic axes instead 

 of one. The rings seen in crystals of two axes are elliptical, when the axes are 

 so far apart that only one can be observed at a time; and they form lemniscate 

 curves, or curves resembling the figure 8, when they are near together. In topaz 



Fig. 24. 



the axes form an angle with each other of G5°, and the rings present the appear- 

 ance shown in Fig. 23, when the analyzer is crossed upon the polarizer, the 

 plane of the axes of the crystal being in azimuth 0° or 90°. This crystal pos- 

 sesses the peculiarity of showing its own rings without the help of an analyzer 

 when the plate subjected to experiment is cut across the line intermediate 

 between the axes, the opposite surfaces being parallel. In such a plate, in order 

 that the ray may follow the line of one of the axes within the crystal, its angle 

 of incidence must be 62j°. The angle of refraction will then be 32^°. The 

 incident angle at either the first or the second surface will, therefore, be very 

 nearly equal to the polarizing angle for the substance, since the reflected and 

 refracted rays make an angle of So*^ with each other ; Avhereas, according to 

 the law of Brewster, at the polarizing angle they should be at right angles. 

 If, therefore, instead of observing the light transmitted through the plate, we 



