CONTEMPORARY ADVANCES IN PHYSICS 307 



length into the speed of Hght. Now all the contemporary theories of 

 the atom and of light are based upon values given for frequencies of 

 radiation; and therefore all of them are founded on the wave-theory 

 of light. 



We will consequently next consider the propagation of waves beyond 

 apertures, or what Rayleigh called the "effects dependent upon the 

 limitation of a beam of light." 



Propagation of a Wave-Motion beyond Apertures 



Suppose that the entire plane x = is occupied by a wall acting as 

 a total stop to all the waves which come up against it, except where 

 it is pierced by one or more openings; and for simplicity suppose that 

 the oncoming waves compose a plane parallel monochromatic train, 



5 = cos {nt — mx), (69) 



advancing from the side of negative x. The primary question is: 

 what goes on in the region to the positive side of the screen? 



The question shall be answered by approximations. 



The first approximation consists in assuming that the wave-fronts 

 come unaltered up to the screen, and each segment which coincides 

 with an aperture goes straight through it and indefinitely onward, 

 travelling unchanged in a straight line even though the surrounding 

 portion of the wave-front has been blocked. If this were perfectly 

 valid, there would be rectilinear propagation of light; the laws of 

 geometrical optics would always be exact; and there would be no need 

 for any but a corpuscular theory of radiation. Because this approxi- 

 mation is deficient, the wave-theory is required. Yet it is close enough 

 to the truth to seem exact to all but the most careful observation, if 

 the apertures are as wide as windows or even as keyholes. 



The second approximation consists in assuming that the wave-fronts 

 come unaltered up to the screen, and each segment which collides with 

 a portion of the wall is swallowed up and blotted out of existence, but 

 the wave-motion within each aperture is precisely the same as it would 

 be if the entire wave-front passed intact across the plane x = 0. That 

 is to say: the displacement on the front face of the screen is supposed 

 to be given thus : 



5 = cos nt, ds/dx = m sin nt wherever there is an aperture, 



. . (70) 



5 = ds/dx = wherever there is obstruction. 



This is the assumption on which are founded the conventional theories 

 of the passage of light through a hole, or a slit, or a pair of slits, or a 



