172 UNDULATOKY THEORY OF LIGHT. 



If WG compare the numbers of uiululations per second in the foregoinj^ table 

 with the numbers per second of acoustic unduhitions corresponding to a given 

 pitcli, we shall observe that, if these vibrations had power to aflcct the sense of 

 hearing, the middle yellow would produce a tone forty-one octaves above the 

 fundamental C, or C between the staves ; and the middle red would be forty 

 octaves above the " Stuttgard pitch," or normal A, taken at 440 comi)lete vibra- 

 tions. The entire interval covered by the visible sjjectrum Avould be about a 

 major fiflh ; between line B and line H, or the part easily visible, a major fourth. 



§ V. DIFFRACTION. 



Wc are now jirepared to understand the causes which produce the stripes or 

 frhiges observed by Grimaldi, bordering the shadows of opaque bodies intro- 

 duced into a divergent pencil of light from a minute radiant point. Let R, Fig. 

 39, be the radiant centre, and PQ the spherical wave front, at any determinate 

 distance from It, as IJ.A. In this case, as in the former, and generally in all 

 analogous experiments, the best radiant for the ])urpose is obtained by concen- 

 trating a small solar beam, (introduced into a dark room,) by means of a lens of 

 short focus. Suppose an o})aque screen S to be advanced to A, so as to inter- 

 cept the half wave AQ. The light which reaches the 

 point B, in the line llA produced, will be the resultant 

 eifect of the unobstructed half wave PA. Let AQ 

 be divided, at a, b, c, 6cc., into parts, such that the 

 lines Ba, Bi, Be, &c., drawn from the point B on a 

 screen BO, to the points of division, may successively 

 exceed each other by the length of one-half an undu- 

 lation ; or such that, drawing the arc AT with B as a 

 centre, the intercepts aa', hh' , cc', &:c., may have 

 the successive values ^A, X, ^X, &c. Now, if the 

 screen S be drawn upward from A to a, the light which reaches B will be the 

 resultant effect of the half wave I'A, combined with the resultant effect of the 

 small additional wave surface Aa. This latter resultant will be compounded 

 of the molecular movements produced at B by the infinite number of minute 

 elementary waves, Avhich may be supposed to originate from all the points of 

 the given Avave front between A and a. Since all these elementary Avaves 

 originate simultaneously, their relatiA'c phases, Avhen they reach B, Avill depend 

 on the differences in the lengths of their paths; and as these differences are the 

 intercepts betAveen the arcs AQ and AT, there Avill be none, until Ave reach a, 

 Avhich will differ from the Avave proceeding from A by so much as half an undu- 

 lation. Assuming, then, that their seA'eral intensities are equal, there Avill be no 

 complete conflict betAvecn any of the elementary AvaA'es Avithin these limits ; and 

 accordingly their resultant effect must be positive, or must add to the intensity 

 of the light at B. If, however, Ave raise the screen S higher, the intercepts 

 Avill begin to exceed half the length of an undulation, and some of the element- 

 ary Avaves originating just b(>yond a will neutralize the effect of some of those near A. 

 liaising it to b, there Avill be a complete series of AvaA'es originating between a 

 and b, which Avill be in absolute conflict Avith the series Avliich originate between 

 A and a ; so that, if Aa and ab Avere exactly equal, and their separate intensi- 

 ties, as above supposed, equal also, their resultant effect at B Avould be zero. 

 Art is, however, a little larger than ab, both because of the inclination of Ba 

 to BA, and because of the curA'ature of AQ. The intensities of the elementary 

 derivative Avaves are also presumed to be greater in the direction of the radius 

 of the original AvaA'e than in directions inclined to it, though the law of such 

 variation of intensity is not known. These causes of difference Avill, neA^erthc- 

 Icss, exist to no A'ery marked degree in the immediate A'icinity of the line IIB, 

 and consequently the total effect at B of the portion of Avave front AZ» will be sen- 

 eibly null. If, noAv, the screen S be further raised to c, the elementary waves 



