DELINEATION OF THE FINE STRUCTURE OF OBJECTS. 229 



If, instead of a single transparent opening, several come into ac- 

 tion, the effect is merely intensified, since all the diffraction pencils, 

 which are inclined to the same extent, necessarily intersect in the 

 same point q of the focal plane, and consequently add to the effect. 

 There would now be an end to the question if we could assume 

 that these pencils did not give rise to any new interferences. 

 In reality, however, this is not the case. The diffraction pencils 

 proceeding from adjacent parts are by no means without influence 

 upon one another. For, in addition to the above-mentioned diffrac- 

 tion lines, new lines are formed in the focal plane which originate 

 through the interference of adjacent pencils. The detailed expla- 

 nation of the phenomena appertaining to this question, especially 

 for any given number of openings, would lead us too far. We 

 must, therefore, refer to the text-books 

 of Physics, 1 or to the detailed exposition 

 of Schwerd, 2 and must confine ourselves 

 here to a brief statement of the facts in 

 question. 



If the transparent openings are nu- 

 merous, and their distances, measured from 

 centre to centre, = d, then the pencils of 

 deflected rays give maxima of brightness 

 for all inclinations at which the difference 

 of path a c (Fig. 126) is equal to one wave- 

 FIG. 126. length, or to a multiple of a wave-length. 



The bright interference lines (spectra of 

 the second order) will therefore appear in those points for which 



X 2X 3X 4X 



sin a = -v 7-* r~ ~~7~> & c '> 

 dad d 



where X again denotes the wave-length and a the angle of deflexion. 



deflected rays which proceed from a single opening will yield bright interference 

 lines for the angles of inclination, whose sines are o x x;2 X ^'2 x A."'** 

 These sines are, therefore, in the ratio of the odd numbers 3, 5, 7, 9, &c. 



1 Vide Wiillners's " Lehrb. der Physik," 2nd ed. In the first edition this 

 matter is erroneously explained. Vide also Verdet's " Le9ons d'Optique 

 Physique," 2 vols. Paris, an excellent work. 



-Schwerd's "Die Beugungserscheinungen," Mannheim, 1835, specially 

 148 and 195, where this is illustrated by diagrams. 



