INTERFERENCE OF POLARIZED LIGHT. 221 



These laws of interference being kept in mind, the rea- 

 son of all the phenomena is apparent. The ray is origi- 

 nally polarized in a single plane, by means of the polarizing 

 plate. It is then divided into two within the crystal, which 

 are polarized in opposite planes ; and these are finally reduced 

 to the same plane by means of the analyzing plate. The two 

 pencils will therefore interfere ; and the resulting tint will 

 depend on the difference of retardation of the two waves, 

 produced by the difference of the velocities within the 

 crystal. 



(230) It is plain that the light issuing from the crystal 

 is, in general, ellipticatty-polarized, inasmuch as it is the re- 

 sultant of two waves, in which the vibrations are at right 

 angles, and differ in phase. Hence, when homogeneous light 

 is used, and the emergent beam is analyzed with a double- 

 refracting prism, the two pencils into which it is divided vary 

 in intensity as the prism is turned, neither, in general, ever 

 vanishing. 



When the thickness of the crystal is such, that the differ- 

 ence of phase of the two rays is an exact number of semi-un- 

 dulations, they will compound a plane-polarized ray at emer- 

 gence, the plane of polarization coinciding with the plane of 

 primitive polarization, or making an equal angle with the prin- 

 cipal section of the crystal on the other side, according as the 

 difference of phase is an even or odd multiple of half a wave. 

 Accordingly, one of the pencils into which the light is divided 



posed to be resolved, without reference to their phase. The justice of this as- 

 sumption depends upon the fact adverted to in the preceding note, namely, 

 that the two oppositely polarized portions, into which we have supposed com- 

 mon light to be resolved, differ in phase, that difference continually varying. 

 The same thing is true, therefore, of the final components ; so that these must 

 be regarded as lights proceeding from different sources, and compound a light 

 equal in intensity to the sum of the components. 



