Theories of Microscopical Vision By A. E. Conrady. 627 



coincidence in the geometrical focal plane ; but the interference 

 between these two waves is evidently not limited to that plane ; 

 interference can and must take place throughout the space, which 

 in the figure has a cross-hatched appearance, where the two waves 

 meet, producing brightness or darkness according to their phase 

 relation at any given point within that space. 



Discussing the question more closely, we know from our pre- 

 vious discussion that in the centre of any line of the image in 

 the plane 1 1 of the geometrical image, the waves from P and P' 

 meet with a difference of a whole number of wave-lengths, thereby 

 producing maximum brightness ; but they will do exactly the 

 same at any point on either side of the plane 1 1 where they meet 

 with the same difference of phase. The geometrical locus for these 

 points is a hyperbola having P and P' as foci, but, owing to the 

 extremely stretched form of the curve, we may with small error 



Fig. 98. 



maximum brightness 



substitute its asymptote, i.e. a straight line connecting any bright 

 point in the plane 1 1 with the point C bisecting the distance 

 between P and P'. There will therefore be 

 along any such line, hence there can be no definite focus 



This is shown in fig. 98, where the zone of possible interference 

 is shown in outline, and the loci, along which maximum brightness 

 would be found, by thick lines. 



It should, perhaps, be pointed out that there may, nevertheless, 

 be something to assist us in picking out the plane 1 1, for fig. 97 

 and fig. 98 show that only close to that plane can the whole extent 

 of the grating be shown : hence it could be focussed for by finding 

 the adjustment showing the maximum number of lines ; but even 

 this expedient would break down with a grating extending beyond 

 the limits of the field of the instrument, or with an object consist- 



