44 



THE INTERFEROMETRY OF 



thick lines, according as one or both spaces were used. If either mirror, M 

 or N, is screened, the whole phenomenon vanishes. 



It follows, then, if rv and v'r', figure 29, represent the two reversed, over- 

 lapping spectra at the grating, b the focus and aa'b the direction of the homo- 

 geneous diffracted rays condensed at b, that about 0.5 cm. of the spectrum, d'a' 

 and ad on either side of a, is chiefly active in modifying the resulting diffrac- 

 tion pattern. Within this the homogeneous rays, cc' and dd', are capable of 

 interference. Although the wave-fronts entering b are slightly spherical, their 

 radius is about r=i meter, and they may therefore be regarded plane. In 

 such a case the angular width d% of the illuminated strip at b, for a width of 

 screen dd' = i cm., between two extinctions, may be written 



_, ff _dx_ \ _6oXio~ 6 

 ~"~r~dd'~ ~ 



= 6Xio- 5 



whereas the angular breadth of the DiD 2 doublets is about 37Xio~ 5 ; i e., 

 the rays from d and d', if in phase, should cease to illuminate b at a breadth 

 of about one-sixth the distance between the sodium lines. The rays within 



d & a 



r. 



a 



28 



I 



6 c d & f 



dd' would correspond to greater widths; those from cc', for instance, 0.5 milli- 

 meter apart, would illuminate twice the estimated width, so that a strip at 

 b, with a breadth of one-third the interval D\D Z , is a reasonable average. All 

 rays, however, would produce illumination at b. As the screens are nar- 

 rower, not only would the fringe be broader, but more lines would appear, 

 because there is less overlapping. All this is in accord with observation. 

 Excepting the occurrence of independent half wave-fronts, the phenomena 

 do not differ from the ordinary diffraction. 



With regard to waves of slightly different lengths, focussed at b', each is 

 there superposed on a wave of different length from its own, and appreciable 

 interference ceases for this reason. If the slit is widened, the phenomenon 

 (with white light) also vanishes by overlapping. The case of the screen with 

 two spaces has already been treated in relation to figure 26. In general, these 

 are cases of the diffraction of a rod, or of a slit, which are possible only if the 

 colors, X, are symmetrically distributed to the right and to the left of it. Thus 

 they require both spectra and can not appear if single spectrum only is present. 

 To reveal the nature of the phenomenon, a wide slit and homogeneous light 

 must be resorted to, as has been done in the present paper, even if white light 

 and the fine slit totally change the aspect of the fringes. 



