DIFFRACTION OF OPAQUE DISK. 17<) 



the radius, is double in area of tlie circle of which Aa" is the radius. But since 

 Ba — I3a''^.y, and Ba" — BA=:^-A, it is obvious that the resultant molecular 

 movement produced at B by the circle of Avhich Aa" is the radius, will be in 

 total conflict with that produced at the same point by the portion ^)f wave front 

 which forms the ring between this circle and the circumference of the orifice. It 

 is this conflict Avhicli produces the dark spot at B. If now a small opaque disk 

 could be introduced into the middle of the oriflce, exactly equal to the circle Aa", 

 stopping out the central pencil of light, B would immediately become bright 

 again. 



If Ba — BA3=4xP-, the circular aperture will be made up of a central 

 circle and three concentric rings, of equal areas, producing movements at B 

 alternately equal and opposite. B will accordingly be obscure. If we stop out 

 now one-half the area in the middle — that is to say, the central circle and the 

 first ring — B will still be obscure ; but if we stop out the central circle and the 

 tico interior rings, the light au B will be restored. Or if Ave stop the central 

 circle only, or, instead of that, the exterior ring, or (which is the same thing) 

 apply over the aperture a smaller one, having only three-fourths the area of the 

 first — in either case the light will be restored. But if we stop the central circle 

 and the outer ring at the same time, B will remain obscure. 



Generally, if Ba — BA=?? X .y, n having any integral cve7i value, the centre 

 of the bright image of the aperture will be dark. If n be odd-cvcn, stopping 

 out one-half the area from the middle of the aperture will restore the light. If 

 n be even-even, stopping out one-half the area will produce no change ; but the 

 light may be restored by stopping a portion of the area Avhicli is by a certain 

 amount greater, or by the same amount less, than one-half. In all these cases 

 the light at the centre, when restored, will be sensibly equal in intensity to that 

 which Avould reach B through an orifice of the size Avhich Avould give 

 Ba"— BA=^A. 



This incidentally leads us to the remarkable result that if, in this experiment, 

 instead of a circular aperture in an opaque plate, Ave employ an opaque disk 

 attached to a transparent plate, 'the centre of the shadow Avill be as highly 

 illuminated as it Avould be if the AvaA^e Avere not interrupted at all. For an open 

 circle Avhose centre and circumference glA'e the relation Ba" — BA=.^A, and 

 a ring whose exterior and interior circumferences give Ba — V)(.J''^=hK pro- 

 duce sensibly the same illumination at B. In either case all the remaining ob- 

 structed portion of the Avave exterior to them may be diAnded into rings, Avliose 

 relation to the unobstructed part will be alternately negative and positive, 

 and Avhose total resultant (Avhich takes the sign of the first term) will be op- 

 posed to that of the unobstructed portion. If then this exterior portion be 

 alloAved to pass, the etiect, in either case equally. Avill be someAvhat to diminish 

 the intensity of the brightness at B, which brightness therefore Avill still remain 

 equal for the circle and for the ring. But in the first instance, this is to alloAv 

 the entire wave to pass; Avhile in the second it IcaA-es the disk. The centre of 

 the shadov/ of the disk, therefore, Avhich is the point B, is as much illuminated 

 as the same point is Avhen the Ava\'e is Avholly unobstructed. This curious cir- 

 cumstance, Avh'.ch Avas first announced by Poisson from theoretic considerations, 

 is easily verified by experiment. 



When it is said that an open circle Avhich gives at its centre and its circum- 

 ference the relation Ba" — BA=?i!X.y-, or a ring of Avhich the outer and inner 

 circumferences furnish a similar relation, will exhibit a dark spot at B whene\^er 

 n is an integral even niunber, it must be remembered that this proposition is 

 true only of the rays AAdiose undulation length is A. If I is the undulation length 

 of the red rays, and >J that of the blue or violet, then at the distance at Avhich 

 red disappears, the blue or violet will not be entirely suppressed. We have 



