Lord Rayleigh's Investigations in Optics. 



267 



This rule is convenient on account of its simplicity ; and it 

 is sufficiently accurate in view of the necessary uncertainty as 

 to what exactly is meant by resolution. Perhaps in practice 

 somewhat more favourable conditions are necessary to secure 

 a resolution that would be thought satisfactory. 



If the angular interval between the components of the 

 double line be half as great again as that supposed above, the 

 brightness in the middle is-1802 (2 x -0901) as against 1*0450 

 (l + *0450) at the central line. Such a falling off in the 

 middle must be more than sufficient for resolution. If the 

 angle subtended by the components of the double line be twice 

 that subtended by the wave-length at a distance equal to the 

 horizontal aperture, the central bands are just clear of one 

 another, and there is a line of absolute blackness in the middle 

 of the combined images. 



On the supposition that a certain horizontal aperture is 

 available, a question (similar to that considered in § 1) arises, 

 as to whether the whole of it ought to be used in order to ob- 

 tain the highest possible resolving-power. From fig. 1 we see 

 that our object must be to depress the curve ABCD at the 

 point B. Now the phase of the resultant is that of the waves 

 coming from the centre ; and at the obliquity corresponding 

 to B the phases of the secondary waves range over half a 

 period. It is not difficult to see that the removal of some of 

 the central waves will depress the intensity-curve at B, not 

 only absolutely, but relatively to the depression produced at 

 A. In order to illustrate this question, I have calculated the 

 illumination in the various directions on the supposition that 

 one sixth of the horizontal aperture is blocked off by a central 

 screen. In this case the amplitude is represented by the func- 



tion/, where ...'/. . u\ ... 



f=u~ l \swu -singj, .... (4) 



and, as usual, the intensity is represented by/ 2 . 



Table II. 



u. 



t 



/ 2 -/o 2 - 



u. 



/. 



r+fo 2 - 







+ •8333 



1-0000 



*« 



-•2729 



•1072 



> 



•7342 



•77G3 



2rr 



•137B 



•0274 



£*■ 



•4717 



•3205 



|w 



-•0307 



•0014 



!*■ 



+ •1377 



•0273 



1 2 

 ■— 77 



•0000 



•0000 



|w 



•0000 



•0000 



|7T 



+ •0043 



•0000 



TV 



-•1692 



•0365 



1 8 



-_ TV 



•0000 



•0000 



j7T 



•3351 



•1617 



~ TT 



-•0329 



•0016 



|7T 



•3622 



. '1889 



3tt 



■1061 



■0162 



