366 SUMMARY OF CURRENT RESEARCHES RELATING TO 



pierced with a series of small apertures. The distribution of light in 

 the focal plane of the eye lens, the view plane, will no longer be 

 uniform ; we shall see the diffraction pattern formed there by the 

 apertures. 



If, for example, there be but one aperture, a single narrow slit, the 

 field will still be uniform ; light diverges from the slit uniformly in all 

 directions, and no structure is seen. 



If we have a number of equidistant slits the view plane will be 

 crossed by a series of equidistant dark and light bars. The distance 

 between these bars and the distribution of light between them will 

 depend on the distance between the slits of the diaphragm and the 

 distribution of luminosity among the slits. If this be known, the dis- 

 tribution of light in the view plane can be calculated. If, for example, 

 the distance between the slits be doubled, the distance between the 

 maxima in the view plane will be halved, that is to say, the number of 

 bright bars in a given interval will be doubled. The distribution in the 

 view plane depends on that in the focal plane, and can be calculated 

 from it ; this is quite certain. 



But now, instead of producing a variable distribution in the focal 

 plane of the object glass by means of diaphragms, we can do it by 

 means of the diffraction effects of small objects on the stage. 



Thus, if we put on the stage a grating consisting of a series of 

 equidistant spaces, and if e be the grating distance, then, taking homo- 

 geneous light, a series of narrow bands of light, the diffraction images 

 of the source, will be produced in the focal plane with darkness between 

 them ; the central image will be on the axis, and if Q x 6 2 . . . be the 

 angular distances between the images, then sin 9 X = X/e, sin 2 = 2X/e, 

 etc. 



It may be shown that the image in the view plane produced by this 

 series of diffracted images is the ordinary geometrical image of the 

 grating. It should be observed that in this proof there is no discussion 

 of the distribution of light in the interspaces between the maxima, and 

 it is on this distribution that the question of resolving power depends. 

 It is clear, of course, that if we modify the number of spectra in the 

 focal plane we modify the image, and this is done in an ingenious way 

 in some of the experiments arranged by Prof. Abbe's pupils to illustrate 

 the theory. 



If we cut out all but the central image the view field is uniform, no 

 structure is visible ; if we allow the first image on either side of the 

 central one to become effective, the bands appear in the field in their 

 proper positions, and so on. It is said to be the fundamental result of 

 Abbe's theory that the object, the grating, can be fully resolved if one 

 diffraction image is formed on either side of the central one. It is clear 

 that in this case there will be variations of intensity in the view plane ; 

 we shall see later what they amount to. 



Now the number of spectra is limited by the fact that some of the 

 diffracted light may be so obliquely diffracted as not to enter the object 

 glass. If 2a be the angular aperture of the object glass measured from 

 the axial point of the stage, then the nth. diffracted image will not appear 

 if sin n is >sin a, but sin 6„ = nX/e. 



