TJie Theory of Optical Images. By Lord Rayleigh. 475- 



cases. Thus a practised astronomer may conclude with certainty 

 that a star is double, although its components cannot be properly 

 seen. He knows that a single star would present a round (though 

 false) disc, and any departure from this condition of things he- 

 attributes to a complication. A slightly oval disc may suffice 

 not only to prove that the star is double but even to fix the lint' 

 upon which the components lie, and their probable distance 

 apart. 



What has been said about a luminous point applies equally to 

 a luminous line. If bright enough, it will be visible, however 

 narrow ; but if the real width be much less than the half wave- 

 length the apparent width will be illusory. The luminous line 

 may be regarded as dividing the otherwise dark field into two- 

 portions ; and we see that this separation does not require a 

 luminous interval of finite width, but may occur, however narrow 

 the interval, provided that its intrinsic brightness be proportionally 

 increased. 



The consideration of a luminous line upon a dark ground is 

 introduced here for comparison with the case, suggested by Mr. 

 Gordon, of a dark line upon a (uniformly) bright ground. Calcu- 

 lations to be given later confirm Mr. Gordon's conclusion that the 

 line may be visible (but not in its true width), although the 

 actual width fall considerably short of the half wave-length. 

 Although in both these cases there is something that may be 

 described as resolution, what is seen as distinct from the ground 

 is really but a single object. So far as I see, there is no escape 

 from the general conclusion, as to the microscopic limit, glimpsed 

 originally by Fraunhofer and afterwards formulated by Abbe and 

 Helmholtz ; but it must be remembered that near the limit the 

 question is one of degree, and that the degree may vary with the- 

 character of the detail whose visibility is under consideration. 



Mr. Gordon comments upon the fact that Helmholtz gave no 

 direct proof of his pronouncement that a grating composed of 

 parallel, equidistant, infinitely narrow, luminous lines shows no 

 structure at a certain degree of closeness, and he appears to regard 

 the question as still open. This matter was, however, fully dis- 

 cussed in my paper of 18 9 G (see above), where it is proved that 

 as the grating interval diminishes, structure finally disappears 

 when the distance between the geometrical images of neighbouring- 

 lines falls to equality with half the width of the diffraction pattern 

 due to a single line, reckoned from the first blackness on one side 

 to the first blackness on the other. It is easy to see that the 

 same limit obtains when the lines have a finite width, provided, 

 of course, that the widths and intrinsic luminosities of the lines 

 are equal. If the grating-interval, that is the distance between 

 centres or corresponding edges of neighbouring lines, be less than 

 the amount above mentioned, no structure can be seen. The 



