CONTEMPORARY ADVANCES IN PHYSICS 319 



This system of annular fringes is the image produced by a lens on 

 which plane-parallel light falls normally through a circular aperture; 

 also when there is no screen before the lens, for being circular it serves 

 as its own aperture. Now plane-parallel light is such as originates in 

 an infinitely distant luminous point, or — what comes to the same thing 

 — any luminous object so distant that neither the curvatures of the 

 wave-fronts proceeding from its various parts nor the angles between 

 the directions in which these lie are appreciably large; a star, for 

 instance. The image of a star in the focal plane of a telescope objective 

 is therefore not a point, however far away the star may be; it is a 

 system of rings. So it is in the eye, the pupil serving as the aperture; 

 but the inner rings are in both cases so narrow and the outer rings so 

 faint that they appear condensed into a point. Magnification of the 

 fringes in the telescope by the eyepiece brings them into view, and so 

 they set a limit to the value of magnification ; for it is of no avail to be 

 able to examine an image more minutely if all that can be examined 

 is the consequence of the disturbance produced in the incoming waves 

 by the finiteness of the lens. 



The limitation which the law of propagation of light thus sets upon 

 the formation of images is very important. The simplest possible 

 illustration is furnished by a double star. Let the telescope be directed 

 upon such a pair of stars so that the light from one component falls 

 normally upon the lens, the light from the other component at any 

 angle of which I denote the complement by (p; thus (p stands for the 

 angular distance between the two stars in the sky. Now I have not 

 hitherto treated the case of light falling otherwise than normally upon 

 the screen containing the apertures, which in this case is nothing but 

 the plane of the objective. The extension however is immediate. 

 Orienting the 3;-axis in the plane of the screen so that the direction of 

 propagation of the waves coming from the stars lies in the xy-p\ane, 

 we have for the wave-function in the region extending up to the 

 aperture from behind : 



5 — COS (nt — mx cos (p — my sin ip), (98) 



and therefore in the plane of the aperture {x = 0) we have, instead of 

 the values given in (71), these: 



5 = cos (nt — my sin (p), 

 ds/dx = m cos (p sin {nt — my sin (p) , (99) 



and for the value of 5 at any point in front of the aperture we have, 

 instead of (77), this value: 



