276 Dr. E. Lommel on the Theory of the 



in all possible directions into the dark space behind the screen 

 may be considered to be grouped into an infinite number of 

 pencils of parallel rays. The one which continues the incident 

 rays is called direct, and the others diffracted', the angle which 

 the direction of a diffracted pencil makes with that of the direct 

 rays is called the angle of diffraction. If there is a lens behind 

 the aperture (the object-glass of a telescope or the crystalline 

 lens of the eye), it will condense the rays of each pencil in one 

 point, which is obtained by drawing a line parallel to the di- 

 rection of the pencil through the optical centre 0, and mea- 

 suring off on this line from the point 0, towards the observer, 

 a length equal to the focal distance of the lens. Hence the 

 points of convergence lie upon a hemisphere drawn from the 

 optical centre of the lens as centre and with its focal length 

 as radius— that is, on the retina in the case of an eye adjusted 

 for an infinite distance. In these points of convergence the 

 rays of all the pencils interfere, in consequence of the differ- 

 ence of path which they have acquired owing to their incli- 

 nation to the direct rays (the action of the lens does not ap- 

 preciably alter the difference of path). The refracted rays, ac- 

 cording to the magnitude of this inclination, sometimes com- 

 pletely extinguish, and sometimes more or less strengthen each 

 other, and thus produce the well-known beautiful diffraction 

 images. For the sake of more convenient investigation, each 

 point of the hemispherical image may be supposed to be pro- 

 jected on the plane base of the hemisphere, and the same inten- 

 sity of light be assigned to it there which it has in the original 

 image. If the incident rays are normal to the plane of the 

 screen, their point of convergence is projected exactly in the 

 centre of that base. From known laws, which need not be de- 

 veloped here, the distances from the centre of the image of equi- 

 valent maxima and minima of luminous intensity, in the case of 

 apertures of similar shapes, are directly proportional to the wave- 

 length of the light used, and inversely proportional to correspond- 

 ing dimensions of the aperture. 



If, then, a diffracting aperture be made gradually smaller and 

 smaller, the commencement of minimum of each colour will be 

 gradually removed further from the middle of the image. Now, 

 as the minima corresponding to the shorter wave-lengths are 

 always nearer the centre of the picture than those belonging 

 to the longer waves, the aperture may ultimately be supposed so 

 small that the first minimum of any colour must commence just 

 at the edge of the surface of the image — that is, for a diffraction- 

 angle of 90°. Then all the less refrangible colours cease to have a 

 minimum ; but one still occurs for each of the more refrangible. 

 If, for example, the breadth of a rectilinear slit be =0*0005888 



