2(>2 Lord Rayleigh's Investigations in Optics. 



tions the intensity is less ; but there will be no sensible dis- 

 crepancy of phase, and therefore no sensible diminution of 

 intensity, until the obliquity is sueh that the (greatest) pro- 

 jection of the diameter of the aperture upon the direction in 

 question amounts to a sensible fraction of the wave-length of 

 the light. So long as the extreme difference of phase is less 

 than a quarter of a period, the resultant cannot differ much 

 from the maximum; and thus there is little to choose between 

 directions making with the principal direction less angles than 

 that expressed in circular measure by dividing the quarter 

 wave-length by the diameter of the aperture. Direct antago- 

 nism of phase commences when the projection amounts to half 

 a wave-length. When the projection is twice as great, the 

 phases range over a complete period, and it might be supposed 

 at first sight that the secondary waves would neutralize one 

 another. In consequence, however, of the preponderance of 

 the middle parts of the aperture, complete neutralization does 

 not occur until a higher obliquity is reached. 



This indefiniteness of direction is sometimes said to be due 

 to "diffraction" by the edge of the aperture — a mode of ex- 

 pression which I think misleading. From the point of view 

 of the wave-theory, it is not the indefiniteness that requires 

 explanation, but rather the smallness of its amount. 



If the circular beam be received upon a perfect lens, an 

 image is formed in the focal plane, in which directions are 

 represented by points. The image accordingly consists of a 

 central disk of light, surrounded by luminous rings of rapidly 

 diminishing brightness. It was under this form that the 

 problem was originally investigated by Airy*. The angular 

 radius 6 of the central disk is given by 



0=1-2197 A ...... (1) 



in which X represents the wave-length of light, and 2R the 

 (diameter of the) aperture. 



In estimating theoretically the resolving-power of a tele- 

 scope on a double star, we have to consider the illumination of 

 the field due to the superposition of the two independent 

 images. If the angular interval between the components of 

 the star were equal to 20, the central disks would be just in 

 contact. Under these conditions there can be no doubt that 

 the star won Id appear to be fairly resolved, since the bright- 

 ness of the external ring-systems is too small to produce any 



* Camb. Phil. Trans. 1834, 



