222 INTERFERENCE OF POLARIZED LIGHT. 



by the analyzing prism will vanish in two positions of its 

 principal section ; and it is manifest that the successive thick- 

 nesses of the crystalline plate at which this takes place form 

 a series in arithmetical progression. 



On the other hand, when the difference of phase is a 

 quarter of a wave length, or an odd multiple of that quantity, 

 and when, at the same time, the principal section of the 

 crystal is inclined at an angle of 45 to the plane of primitive 

 polarization the emergent light will be circularly polarized. 

 This is one of the simplest means of obtaining a circularly- 

 polarized beam ; but it has the disadvantage, that the required 

 interval of phase is only exact for waves of one particular 

 length, and that therefore the circular polarization is perfect 

 only for one colour. 



(231) We may now calculate the intensities and the 

 tints of the two emergent pencils, when a parallel pencil of 

 polarized light is incident upon a thin crystalline plate, and 

 the emergent pencils transmitted through an analyzing rhomb 

 of Iceland spar, or any other double-refracting crystal. 



Let the first surface of the crystalline plate be imagined to 

 lie in the plane of the paper, and from the' point of incidence, 

 0, let the line OP be the section with that plane, of the 

 plane of primitive polarization of the ray, and OA its inter- 

 section with the principal plane of the crystal ; and let the 

 angle which it forms with the plane of primitive polariza- 

 tion, POA = a. Finally, let OB be the intersection with the 

 same plane of the principal plane of the analyzing rhomb ; 

 and let the angle which it makes with the plane of primitive 

 polarization, POB = /3. On entering the crystalline plate, 

 the polarized ray will be divided into the ordinary ray, 0, 

 whose amplitude of vibration is represented by cos a, the 

 amplitude of the original vibration being taken as unit ; and 

 the extraordinary ray, E, whose amplitude is proportional to 



