564 Prof. Chuckerbutti on Deformation of " Rings 



plane of polarization vertical and the polarizer horizontal. 

 In fig. 1 the crystal is placed so that the twinning layer 

 extends vertically up and down, inclined in such a manner 

 that its sections with the faces o£ the crystal are vertical 

 straight lines. Light is always allowed to fall normally 

 upon the first face of the crystal, as otherwise the three 

 images of which mention has been made before will make 

 the system more complicated. Figs. 2, 3, 4 are obtained by 

 rotating the crystal to the left in its own plane till the rota- 

 tion amounts to 7r/2, when the system corresponds with fig. 1 

 but rotated through 90°. As we proceed further beyond 7r/2, 

 the figures 2, 3, 4 come in the reverse order, fig. 4 being- 

 followed by figs. 3 and 2 and at it we get back to fig. 1. 

 On rotating further, figs. 2, 3, 4 come in turn, similarly as 

 in the first quadrant, and the figure at 37r/2 corresponds with 

 the one at tt/2. The order of succession of the system along 

 the last quadrant corresponds with that of the second quad- 

 rant. Figs. 5 to 8 were obtained by rotating the tourmalines 

 in some position other than the crossed and at the same time 

 rotating the crystal also. In general, the systems are rather 

 cumbrous in these cases and the four cases are selected out, 

 as showing the changes rather systematic.! lly. Figs. 7 and 8 

 have the peculiarity that they are complementary in nature 

 to figs. 4 and 1 respectively, although they were obtained 

 when the tourmaline planes were not parallel but inclined at 

 an angle of about 45°. 



4. Physical Theory. 



In general, if & be the path retardation of two rays due to 

 their passage through a uniaxal crystal the equation to the 

 generating curve to the isochromatic surface is 



where the opric axis lies along the axis of X. 



In case of a regular crystal of thickness T, the section of 

 the isochromatic surface by a plane x = T gives the equation 

 for the rings, and the points giving the same path-retardation 

 are equidistant from the centre of the system. Now the 

 interposition of the thin layer which again has its optic axis 

 inclined to the optic axis of the main crystal, causes different 

 path-retardation upon the interfering rays, so that the points 

 of equal path-retardation are not equidistant from the centre^ 

 :ind as a result we should expect distorted curves. 



