Phenomena of Crystals and Circularly Polarized Light, /l 



90° of rotation ; and if the analyzer be turned in the same direction, 

 the colours change, but in the reverse order. The explanation of 

 this is to be found in the fact that when the plates A and B are 

 crossed, the retardation due by A is compensated by that due to B ; 

 so that the only effective retardation is that due to the crystal C. 

 But upon this depends the rotation of the plane of polarization ; if, 

 therefore, the polarizer and analyzer remain fixed, the colour will 

 remain unaltered. When the plates A and B have their axes parallel 

 there is no compensation, and the colour will consequently change. 

 This experiment was made by Fresnel. The mathematical expres- 

 sions for the intensity of the light in the two cases respectively are 



cosMy+« + 7-,Y and cos=n'~/— -Y 



where i is the angle made by the principal sections of A with that 

 of the polarizer, and j that of the principal section of B with that 

 of the analyzer. The first expression is obviously unchanged when 



the angle between the polarizer and analyzer, viz. - + ?+/, is 



unchanged. 



It should be added that the rotation of the plane of polarization, 

 and consequently also the sequence of tints, does not follow exactly 

 the same law in the above cases as in quartz. 



We now come to the case of convergent light — that is, to the 

 phenomena of crystal rings ; and let us examine the effects produced 

 by the same arrangement as before, viz. two quarter-undulation 

 plates A, B, one in front and one behind the crystal C. To quote 

 from Mr. Airy : — " The first thing that strikes us in this combi- 

 nation is that there is nothing, except in the crystal, that has any 

 respect to sides. For the only incident light is circularly polarized ; 

 the only light allowed to emerge is circularly polarized. The ap- 

 pearance therefore of the coloured rings &c. must be such as conveys 

 no trace of any plane of polarization, and must not vary as the 

 crystal is turned round. In the common exhibition of the coloured 

 rings the principal trace of the planes of polarization is in the un- 

 coloured brushes. In uniaxial crystals they form an eight-rayed 

 star, composed of two square crosses, inclined at any angle equal to 

 that between the planes of polarization, every ray of which sepa- 

 rates complementary rings. In biaxial crystals they compose two 

 pairs of rectangular hyperbolas, the angle between whose asymptotes 

 is the same as that between the planes of polarization, and whose 

 branches divide complementary rings. The two crosses or two sets 

 of hyperbolas unite when the planes of polarization are parallel or 

 perpendicular. But in the case under consideration the rings exhi- 

 bited by crystals will not be traversed by any brushes. Uniaxial 

 crystals will exhibit circular rings without a cross ; and biaxial 

 crystals will exhibit complete lemniscates, without any interruption 

 from curved brushes." And it is further to be noticed, as the 

 formula given above indicates, that the centres of the rings will be 

 bright or dark according as the analyzer stands at 0° or 90°. 



