208 FRESNEL. 



In order that the difference of route alone may deter- 

 mine whether two rays of the same origin and the same 

 colour shall reinforce or destroy each other, it is neces- 

 sary that both should be traversing the same medium, 

 solid, liquid, or gaseous. If it be not thus, we must then 

 also take into account (as a member of the Academy* 



and similarly for successive values of c, measured from the central 

 point, involving successive multiples of A; and if a plate of glass 

 whose refraction index is p, be interposed in the path of one of the 

 rays, whose thickness is i, the difference of retardation will be equiv- 

 alent to a difference of route expressed by 



d = t(pl) 



and this being substituted for the 'particular multiple of A, which 

 expresses the difference of routes in the first formula, gives for the 

 displacement 



, \ cot 6 

 c = t(p 1) - 



a 



It may be added that the values of the wave lengths determined by 

 this method from the observed widths of the stripes, or by others of 

 an analogous kind, give results exactly accordant with those long ago 

 assigned by Newton for the length of the "fits" derived from his 

 measures of the diameters of the coloured rings, and by which, from 

 the known curvatures of the lenses, he determined the thickness of 

 the films, and thence the lengths of the " fits." Translator. 



* The retardation of one of the rays, and consequent shifting of the 

 stripes, is here alluded to, which was the discovery of Arago; being 

 in the first instance exhibited by the total disappearance of the stripes, 

 as must be the case if the plate of glass have more than almost an in- 

 finitesimal thickness. The fact was first announced as a sort of par- 

 adox, that as Young had found the stripes entirely disappear by inter- 

 posing an opaque screen on one side only, so Arago produced the same 

 effect with a perfectly transparent screen. In order to explain this 

 effect, let us conceive the simple case of two rays of white light, made 

 to interfere a? in Fresnel's experiment. 



The slightest consideration Avill show that, at the middle point of 

 the mixture of light, two concurring rays, of whatever primitive col- 

 our or wave length, have gone through precisely the same length of 

 route; and thus the central stripe and its immediate neighbour on 

 each side, are absolutely white and black, and perfectly defined; but 

 in proportion as we recede from this point on either side, the differ- 



