INTERFERENCE OF POLARIZED LIGHT. 



the sines of the angles made by the normal to their front with 

 the two optic axes. But, in the case of 'a parallel plate, it 

 may be shown, the difference of the squares of the velocities 

 is proportional to the thickness of the plate multiplied by 

 the interval of retardation. Hence in the case of uniaxal 

 crystals, for a given plate, the interval of retardation is pro- 

 portional to the square of the sine of the angle which the ray 

 makes with the optic axis within the crystal. It may be 

 easily shown that the sine of this angle is very nearly pro- 

 portional to the sine of the angle LEO (see first fig. p. 227), 

 which the emergent ray makes with the axis ; and this latter 

 to LO, the distance of the point of emergence from the cen- 

 tre. The retardation therefore varies as the square of the 

 distance LO ; and consequently the successive dark and 

 bright lines will be arranged in circles (as represented in the 

 preceding diagrams), the squares of whose radii are in arith- 

 metical progression. 



We have been speaking hitherto of homogeneotis light. 

 When white or compound light is used, the rings of different 

 colours will be partially superposed, and the result will be a 

 series of iris-coloured rings separated by dark intervals. All 

 the phenomena, in fact, with the exception of the cross, are 

 similar to those of Newton's rings ; and we now see that 

 they are both cases of the fertile principle of interference. 

 These rings are exhibited even in thick crystals, because the 

 difference of the velocities of the two pencils is very small 

 for rays slightly inclined to the optic axis. 



(236) Let us now consider briefly the case of biaml crys- 

 tals. 



Let a plate of such a crystal be cut perpendicularly to the 

 line bisecting the optic axes, and let it be interposed, as be- 

 fore, between the polarizing and analyzing plates. In this 

 case the bright and dark bands will no longer be disposed in 



