INTERFERENCE OF POLARIZED LIGHT. 225 



This equation is fulfilled, when sin 2a = 0, i. e., when 

 a=0, or a = 90; 



or the principal section of the crystal either parallel or per- 

 pendicular to the plane of primitive polarization. 



The same condition is fulfilled, independently of a, when 

 sin 2 (a-/3) = 0, i. e., when 



a -|3 = 0, ora-j3 = 90; 



or the principal section of the analyzing prism parallel, or 

 perpendicular to, the principal section of the crystal. 



These consequences of the formulas are also evident from 

 the consideration, that in each of the cases referred to, one 

 of the resultant pencils vanishes, and there is, consequently, 

 no interference. 



The coloration is greatest when the coefficient of the quan- 

 tity sin 2 TT ( r j, is a maximum, or sin 2a sin 2 (a - /3) = 1, 



i. e., when 



a = 45 ; 



/3 = 0, or /3 = 90. 



To produce the most brilliant effects of colour, therefore, 

 the principal section of the crystal should form half a right 

 angle with the plane of primitive polarization, while the 

 principal section of the analyzing prism should be either 

 parallel, or perpendicular to, that plane. The intensities of 

 the ordinary and extraordinary pencils in this case are 



(o -e 



COS 2 7T -r 



V A 



When the angles a and /3 are unchanged, the intensity 

 of the light of the two pencils varies only with the quantity 



