2(>4 Lord Rayleigh's Investigations in Optics. 



We have scon that a certain width of beam is necessary to 

 obtain a given resolving-power ; but it does not follow that the 

 whole of an available area of aperture ought to be used in order 

 to get the best result. As the obliquity to the principal direc- 

 tion increases, the first antagonism of phase which sets in is 

 between secondary waves issuing from marginal parts of the 

 aperture ; and thus the operation of the central parts is to retard 

 the formation of the first dark ring. This unfavourable influ- 

 ence of the central rays upon resolving-power was well known 

 to Herschel, who was in the habit of blocking them off by a 

 cardboard stop. The image due to an annular aperture was 

 calculated by Airy ; and his results showed the contraction of 

 the central disk and the augmented brightness of the surround- 

 ing rings*. More recently this subject has been ably treated 

 by M. Ch. Andre f , who has especially considered the case in 

 which the diameter of the central stop is half the full aperture. 

 How far it would be advantageous to carry the operation of 

 blocking out the central rays would doubtless depend upon the 

 nature of the object under examination. Near the limit of the 

 power of an instrument a variety of stops ought to be tried. 

 Possibly the best rays to block out are those not quite at the 

 centre (see § 2). 



The fact that the action of the central rays may be disad- 

 vantageous shows that in the case of full aperture the best 

 effect is not necessarily obtained when all the secondary waves 

 arrive in the same phase at the focal point. If by a retarda- 

 tion of half a wave-length the phase of any particular ray is 

 reversed, the result is of the same character as if that ray were 

 stopped. Hence an exactly parabolic figure is not certainly 

 the best for mirrors. 



The character of the image of a luminous line cannot be 

 immediately deduced from that of a luminous point. It 

 has, however, been investigated by M. Andre, who finds that 

 the first minimum of illumination occurs at a somewhat lower 

 obliquity than in the case of a point. A double line is there- 

 fore probably more easily resolvable than a double point ; but 

 the difference is not great. In the case of a line the minima 

 are not absolute zeros of illumination. 



§ 2. Rectangular Sections. 



The diffraction phenomena presented by beams of rectan- 

 gular section are simpler in theory than when the section is 

 circular ; and they have a practical application in the spectro- 



* See also Astron. Month. Notices, xxxiii. 1872. 



t " Etude de la Diffraction dans les Instruments d'Optique," Ann. ch 

 VEcole Norm. v. 1870. 



