228 INTERFERENCE OF POLARIZED LIGHT. 



cides with, or is perpendicular to, the plane of the first 

 reflexion. In the latter case, therefore, a black cross will be 

 displayed on the field, and in the former a white one, as is 

 represented in the annexed diagrams. 



But the case is different with the rays which emerge at 

 any other point, such as L. The principal section of the 

 crystal for this ray, OL, neither coincides with, nor is per- 

 pendicular to, the plane of primitive polarization ; and con- 

 sequently the incident polarized ray will be divided into two 

 within the crystal, whose planes of polarization are parallel 

 and perpendicular to OL, respectively. The vibrations in 

 these two rays are reduced to the same plane by means of 

 the analyzing plate : they will therefore interfere, and the 

 extent of that interference will depend on their difference of 

 phase. 



Now the difference of phase of the two vibrations depends 

 on the interval of retardation. When this interval is an odd 

 multiple of half an undulation, the two vibrations are in 

 complete discordance ; and, on the other hand, they are in 

 complete accordance when it is an even multiple of the same 

 quantity. We have seen (216) that, in general, the diffe- 

 rence of the squares of the velocities of propagation of the 

 two waves within a crystal is proportional to the product of 



