70 Royallnstitution : — Mr, W. Spottisvvoode on Optical 



ization by the principal sections of the crystal and of the analyzer 

 respectively, and d is the retardation. 



If, however, the two quarter- undulation plates (say the plates A 

 and B) be introduced, the light undergoes the following processes : — 

 First, it is plane-polarized by the polarizer; secondly, the plate A 

 being placed so that its axis is inclined at -1-45° to the original plane 

 of polarization, the light undergoes right- or left-handed circular 

 polarization, and in that condition falls upon the crystal ; thirdly, in 

 their passage through the crystal C the rays are each divided into 

 two, whose vibrations are at right angles to one another, and whereof 

 one is retarded in proportion to the thickness of C ; fourthly, the 

 plate B being placed so that its axis is parallel or perpendicular to 

 that of A, each of these sets of rays is circularly polarized, one set 

 right-handed and the other left-handed ; fifthly, these two oppositely 

 circularly polarized sets of rays combine, according to known me- 

 chanical laws, on emerging from B into plane rays, in which the 

 planes of polarization of the diflPerent colours of the spectrum are 

 turned through different angles. Hence, finally, by turning the 

 analyzer round we shall cross these various planes in turn and 

 successively extinguish the difi*erent colours, leaving the comple- 

 mentary colours visible. The system'of plates A, C, B consequently 

 acts in this respect like quartz. It is, however, to be observed that 

 if the plate B be turned from one of the two proposed positions to 

 the other, the directions of motion in the two emergent circularly 

 polarized rays, and consequently the planes of polarization of the 

 diff'erent colours, will be reversed ; in other words, with the plate B 

 in one position we shall imitate a right-handed, with the plate B in 

 the other a left-handed quartz. The intensity of the light at any 

 point is then given by the formula 



a 



sin^-for one position. 



Again if, the plates A B retaining either of the positions before 

 indicated, the crystal C be turned round in its own plane, then, 

 since the light emerging from A and B is circularly polarized, it has 

 lost all trace of direction with reference to the positions of the 

 polarizer and analyzer, and consequently no change of tint will be 

 observed. The same is abundantly clear from the formula written 

 above, because the only term it contains depends upon the retar- 

 dation within the crystal C. This experiment was made by Airy. 



If the plates A and B have their axes directed 45° on either side 

 of the axis of C, and the three plates be turned round as one piece, 

 the colour will remain unchanged ; w^hile, if the analyzer be turned, 

 we have the colours shown in the regular order. If the plates A and 

 B have their axes directed at 45° on the same side of the axis of C, 

 and the pieces be turned round bodily as before, the colours change 

 in the same order as above, and go through their cycle once in every 



