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X. On Pin-hole Photography. 

 By Lord Rayleigh, Sec. R.S.* 



[Plate IV.] 



IT has long been known that the resolving power of lenses, 

 however perfect, is limited, and more particularly that 

 the capability of separating close distant objects, e. g. double 

 stars, is proportional to aperture. The ground of the limita- 

 tion lies in the finite magnitude of the wave-length of light 

 (X), and the consequent diffusion of illumination round the 

 geometrical image of even an infinitely small radiant point. 

 It is easy to understand the rationale of this process without 

 entering upon any calculations. At the focal point itself all 

 the vibrations proceeding from various parts of the aperture 

 arrive in the same phase. The illumination is therefore here 

 a maximum. But why is it less at neighbouring points in 

 the focal plane which are all equally exposed to the vibrations 

 from the aperture ? The answer can only be that at such 

 points the vibrations are discrepant. This discrepance can 

 only enter by degrees ; so that there must be a small region 

 round the focus at any point of which the phases are practi- 

 cally in agreement, and the illumination sensibly equal to the 

 maximum. 



These considerations serve also to fix at least the order of 

 magnitude of the patch of light. The discrepancy of phase 

 is the result of the different distances of the various parts of 

 the aperture from the eccentric point in question ; and the 

 greatest discrepancy is that between the waves which come 

 from the nearest and furthest parts of the aperture. A simple 

 calculation shows that the greatest difference of distance is 

 expressed by 2rx/f, where 2r is the diameter of the aperture, 

 f the focal length, and x the linear eccentricity of the point 

 under consideration. The question under discussion is at 

 what stage does this difference of path introduce an important 

 discrepancy of phase ? It is easy to recognize that the illu- 

 mination will not be greatly reduced until the extreme discre- 

 pancy of phase reaches half a wave-length. In this case 



2*=A/2r, 



which may be considered to give roughly the diameter of the 

 patch of light. If there are two radiant points, the tw r o repre- 

 sentative patches will seriously overlap, unless the distance of 

 their centres exceed 2x. Supposing it to be equal to 2x, 

 which corresponds to an angular interval 2x/f, we see that 



* Communicated by the Author. 



