CONTEMPORARY ADVANCES IN PHYSICS 



185 



reinforce each other; this is the explanation of the central bright fringe. 

 At any point not quite equally distant from the slits, they do not 

 arrive quite simultaneously, and the reinforcement is impaired. But 

 at a point which is further from one slit than from the other by just 

 the wave-length X, the wave crest arriving from the latter meets the 

 next previous crest from the former, and the reinforcement is re- 

 stored. The first-order maximum is located at these points. 



Fig. 4. 



From Fig. 4 one sees ''^ that when the screen is very far away, the 

 points distant from the slit 6\ by one wave-length more than they are 

 distant from S-i are situated in the direction inclined at to the straight- 

 ahead direction, the angle being given approximately by the formula 



sin 4> = ^,<3, 



(46) 



where a stands for the distance between the slits. When the screen is 

 infinitely far away, the formula is exact. (I must admit that it is 

 somewhat disingenuous to simplify the problem by solving only the 

 special case in which the screen is infiniteh' far away, for the general 

 case opposes much more serious difiiculties to the corpuscle- theory-; 

 but this is the special case of greatest physical importance, and one has 

 to make a beginning somewhere.) 



We have now explained the presence of a first-order maximum in 

 the pattern of light and shade on the screen, though it cannot be said 

 that we have "verified" formula (46), for that formula serves as the 

 practical definition of wave-length : wave-lengths are measured by 



'■' From the figure wq see that for di and d>, the distances from .S'l and 6- to the 

 point P on the screen, we have: 



d{- = D' + X-, dy = D' + (.V - a)\ d, = D sec <^, .v = D tan <^ 



and hence 



(d, - d-i)(d, +<f,) = lax - a\ 



When D, x, di and </•: all become infinite together, the second factor on the left becomes 

 equal to 2D stc ^ and the second term on the right may he neglected. 



