414 Professor Airy on the Phenomena 



we have ?„. = °> whence g = e: and the intensity in the central 

 rrp) . The condition g=e gives 



tan (i — i" ) _ tan (« — Q 

 tan («' + <") ~ tan (< + «') ' 



whence sin 2 2i = sin 2«. sin 2i" : 



or COS 2 i' = : COS ( . COS l" 



mm 



where m and mi are the refractive indices of the two media. 

 Without attempting to solve this equation generally, suppose 

 »j = 1,53 and »a' = 2,45 (which correspond nearly to plate glass and 

 diamond). The values oft' at the polarizing angles are 56". 49'. 54" 

 and 67°. 47'. 48"; and the value of «' which makes the first ring 

 black is 63". 19'. 4" ; the values of t and «" corresponding to this are 

 35". 43'. 57" and 21°. 23. 21": whence e =g= 0,083215 ; and the in- 

 tensity of the light at the central spot = « s x 0,02732. 



But to obtain a practical idea of the import of this expression 

 we must compare it with the intensity of light in the rings 

 in some other position. Now when the incidence is perpendicular, 

 the expressions above give for the difference of the light in the 

 dark spot and bright rings, a- x 0,28159. Consequently the inten- 

 sity of light in the rings seen between the two polarizing angles 

 is less than one-tenth of that in the rings seen at a nearly per- 

 pendicular incidence. As the latter are by no means vivid, we 

 must expect the former to be faint. 



The intensity of the rings which would be produced at the same 

 angle of incidence by light polarized in the plane of reflection, 



found in the same way, (putting <?'= ." .' , ',[ and g'= sm ,,~ '„ ) 



3 V s sin(i + «) s sin(i' + <)/ 



