10 Rheinberg: Common Basis ofthe Theories ofMicroscopic Vision. XIX, 1. 



that it depends amongst other things on the diameter of the wave 

 front emerging from the lens. For if in fignre 4, the wave front 

 were half as wide , extending only from J^ to C instead of to Y^ 

 then a line drawn from C to B would be half a wave length longer 

 than J^B^ and we should have precisely the State of things which 

 is depicted in figure 3 , except that i? would now take the place 

 of (J. 15ut B is about twice as far off from P', the centre of the 

 dise, as () is 5 so that by halving the emergent wave front we have 

 donbled tlie extension of the disc ; and in like manner it can be 

 Seen that any extension of the effective aperture ^ of the lens 

 or emergent wave front is foUowed by a contraction of the disc 

 and its rings. They foUow the simple law of inverse ratio. Observe 

 how in ligure Q j Q in abont -| the distance from P' that it is in 

 figure 2 , because the distance P' to the lens is only | as long. 

 With regard to actual measurements , it will suffice for the present 

 to mention that at a distance from the lens of 250 mm (10 inches) 

 in Order to get the first bright ring separated from the disc by 

 about j\y mm (-^^j)") — a Separation not resolvable by the naked 

 eye — the effective aperture of the lens must already be cut down 

 to less than 2 mm, 



Thus far we liave assumed several things: 



1) That the centre of disturbance was confined to an iso- 

 lated point. 



2) That light of one colour (ndy was beiug propagated at 

 the centre of disturbance. 



?)) That the wave front on emergence from the lens was 



absolutely spherical, i. e. that the lens is entirely free 



from spherical aberration. 



With regard to the first matter, when, as is usually the case, 



the source of illumination has finite dimensions large as compared 



to wave lengths of light, each point of the same forms its own disc 



and ring, and we get a whole series of them overlapping one another. 



The brightest spot of one disc corresponds in position with a less 



bright part of the next, a still fainter part of the next, and so forth. 



8ui)pose for a moment equidistant points on the disc were 



represented by 6, 10, 6, and consider the effect of a number of such 



discs overlapping thus : 



') Aperture is here used in its primitive meaning of the diameter of 

 the opening of the lens. 



