CONTEMPORARY ADVANCES IN PHYSICS 401 



distances from any atom-group ^ to P and Q, by ri and ^2 the distances 

 to these points from the adjacent group B. We shall not assume 

 that Ri, Yi are coplanar with R^, r^, though owing to the flatness of 

 the page the drawing must make them seem so. Denote by </>, 6 the 

 angles between the direction of the row of atom-groups and the 

 directions in which the primary and the scattered waves advance, 

 respectively — these latter being the directions from A aivay from P 

 and towards Q, respectively. 



Under what condition will the waves scattered by the atom-groups 

 A and B reinforce one another best at Q? Best reinforcement will 

 occur, greatest enhancement of the effect of either atom by the 

 presence of the other, when the waves from both arrive at Q in identical 

 phase. This will occur when Q is so located that the path from P to 

 Q via A either is equal to the path from P to Q via B, or differs from 

 it by an integer number of wave-lengths.* 



(i?i + i?2) - (n + r^) = {Rx - r,) -f (i?o - rs) = «X; 



w = 0, ±1, ±2, . . . (1) 



Let P and Q recede to infinity; in the limit: 



Ri — rx = a cos 0, R2 — r^ = —a cos d (2) 



and the condition for optimum reinforcement at Q is this: 



a (cos 6 — cos <^) = n\. (3) 



In all directions for which d satisfies this equation, there will be 

 maximum amplification of the diffraction-pattern of A (or B) by the 

 presence of B (or A). For every such value of 6, there will be a ring 

 on the wall of the bulb. If the two atom-groups by themselves could 

 make the wall fluoresce brightly enough, we should see annular 

 fringes. They would be broad and hazy, for though the cooperation 

 between the scattered waves is best at the definite angles determined 

 by equation (3), it is also very good over quite a range of nearby 

 angles. Equation (3) would give the locations of the central rings of 

 the broad fuzzy bright fringes. Thus, when visible light is sent 

 through a pair of parallel similar slits in a screen, one sees hazy fringes 

 superposed on the diffraction-pattern which either slit by itself can 

 produce; and the formula analogous to equation (3) locates the 

 central lines of these. 



^ This statement implies the tacit assumption that there is a constant phase- 

 difference (whether it is zero or not is of no importance) between the primary waves 

 striking an atom-group and the scattered waves leaving it — the very important 

 assumption of coherence. 



