M. Mascart on the Achromatism of Interference!^. 523 



and we have 



df 2x . ^f g . . 



The condition for achromatism becomes 



/cos i sin t sin A \ _ hx sin A , . 



\ L cos (/8— i) cos?''/ B, cosicos (/S— «') cos?-'* * ^ ^ 



This curious fact also presents itself, that the final equation 

 which will give one of the unknowns, such as ,x or 6, is not 

 of the first degree ; thus there may exist several distinct 

 achromatic fringes and several groups of visible fringes. 



If, for example, we make /=0, which corresponds to vision 

 along the normal to the surface, equation (7) reduces to 



^2 _ 2/, L — ^^^A_, ^ + 2R^o = 0. 

 cos p cos r 



The problem is possible only when the condition 



COS'' p COS r 



is satisfied, and the two corresponding values of a; are in this 

 case positive. 



One of these values is zero for ^o = 0. If, therefore, under 

 these conditions, we observe ordinary coloured rings by means 

 of a prism, the central spot remains achromatic, and we per- 

 ceive at some distance a group of branches of rings, the more 

 compact and the more numerous the higher the order of the 

 achromatized fringe. This is Newton's experiment. 



3. If the interference takes place between plane waves, as 

 in Jamin's apparatus, the rings produced by diffusion in tliick 

 plates, the phenomena of chromatic polarization in thin plates 

 wdth parallel faces, &c., we must replace equations (1) by the 

 following: — 



A = mX = /(O, 1 



-0=6 -i = </)(i»,j ^^ 



which amounts simply to suppressing the variable x. 



The order of the achromatic fringe, and the angle of diver- 

 gence of the neighbouring fringes, are in this case determined 

 by the equations 



mX_^f sin A 

 Lt~"di cos {/3—i) cos /•" 



,^ L sm A 



do= — = 



m 



(9) 



