On an Optical Paradox. 127 



and they in no degree depend upon phase relationships 

 between the puncta of A, the enlarged source of light. 



Lord Rayleiglr's experiment is one familiar to the present 

 writer, whether made with a collimator, an intermediate lens 

 and a telescope; or with a microscope : he prefers the latter 

 form of the experiment, as it lends itself more conveniently 

 to an investigation of the successive phenomena with the 

 powerful aid of an analysis of the light into its component 

 undulations of flat wavelets. The experiment is one of those 

 which it has been his intention to describe and explain in the 

 next of the series of papers on " Flat- wavelet Resolution " 

 which is being published by the Phil. Mag. The full dis- 

 cussion will be postponed till that paper appears ; but some 

 of its results may in anticipation be stated here. 



The analysis into undulations of flat wavelets makes it easy 

 to understand the way in which the image of L is formed in 

 telescope T. It is formed by the mutual interference of all 

 the undulations of flat wavelets which advance in the direc- 

 tions indicated by the so-called " rays w that pass into the 

 telescope from the several optical puncta of the image of A 

 produced at C by lens L. In the case where the source of 

 light is a single punctum or physical point, this image con- 

 sists of a distribution of light upon which is nearly* Airy's 

 " spurious disk " along with its diffraction appendages. 



Telescope T is to be focussed on L, and then, in order that 

 the observer may be able to distinguish between the parts of 

 an object so small as lens L (and, therefore, to exhibit the 

 outline of that object), the analysis indicates that, if A the 

 source of light be a single luminous punctum, the aperture 

 of the telescope-objective C must take in, in addition to the 

 spurious disk, some part of the appendage rings ; or else 

 portions of two or more of these rings if all light from the 

 spurious disk is excluded. 



To exhibit lens L in the most satisfactory way the aperture 

 of objective C must be large enough to include the spurious 

 disk and all its diffraction appendages that have any appre- 

 ciable brightness. If the objective be anything smaller than 



* Conceive the lens L to be divided into two lenses L' and L", of 

 which L' parallelises the light from the point source A, and L" concen- 

 trates this approximately parallel beam to a focus at C. Then the image 

 at C woidd be exactly Airy's image, if the parallelised beam were an 

 exact beam of parallel light ; but this it cannot be, since it can be shown 

 that to form an exact parallel beam would require a small amount of 

 other light than that from A to be incident upon lens L'. Accordingly, 

 the light which is concentrated by L" upon C is only an approximately 

 parallel beam of light, and the image it forms differs slightly from Airy's 

 image of a star. 



