137 



?i-H„=±«.— , (10) 



wliere 5 is a moderate number, tlie absorption is much smaller than 

 for 11 — ?ï„. Hence, the absolute value of (10) will give us some idea 

 of half the v^^idth of the absorption band. The smaller the coefficient 

 of resistance, the narrower the band is seen to be. A strong maxi- 

 mum of absorption and a small width will be found together, whereas 

 in the case of a feeble maximum we shall find a broad band. 



For values of n, differing so much from n„ that ing may be 

 treated as a small quantity compared with m{n„^ — n^), we may 

 replace (6j by 



((xY = 1 H i—. 



m(n^'—n^) ni''(n„^ — n^Y 



.Supposing further that the real part on the right hand side is 

 positive and much greater than the imaginary one, we find approxi- 

 mately 



Ne' 



1 + 



«(«„'— w') ' 



_ NeV 



~ 2nctn'{n„'—nY ^' 



The last formula shows that the absorption at a rathei" large 

 distance from the maximum increases with tlie coefficient of resist- 

 ance, just the reverse of what we found for the maximum itself. 



For values of </, so great that «<^<^1, the equations become less 

 complicated. Indeed, for this case (6) may be written 



1 Ne' 



(fi) = 1 + - . 



2 /«(?(/—«') +tn£)i 



and this, combined with (4), leads to the values 

 1 Ne'm{n,^—n') 



fi=l + 



2 -„jv-vr + wy' 



_ 1 Ne^ii^g 



This last equation shows that for n = n„ 



_Ne' 



agreeing with (8), and that at the distance from the maximum deter- 

 mined by (10), the index of absorption has become s'' -\- 1 times 

 smaller than /*„. 



