PHOTONS AND ELECTRONS 9 



and bounce out of their paths, but actually no such sidewise scattering 

 of one beam by another is observed, and this can be interpreted by saying 

 that the corpuscles are so excessively small that collisions are too rare to 

 be appreciable.) What is observed is different: In the region common 

 to the two beams there is a peculiar distribution of light intensity known 

 as a "system of fringes," the intensity varying from point to point accord- 

 ing to the formula 



Intensity « 1 + cos {2my sin 0) (7) 



where m stands for a constant to be determined by measurements of the 

 pattern {e.g., by measuring the distance between two consecutive "dark 

 fringes" or lines of vanishing intensity, which are obviously parallel to 



the X-axis and are separated^ by distances -. — )• Now this is exactly 



nt/ St/it (p I 



the law of variation of the squared amplitude of the wave pattern occur- 

 ring when two identical sine-wave trains intersect one another at angle 

 2ip. Suppose the amplitude, frequency, and wave-length of each to be 

 denoted by A, n/27r, and X, respectively, and denote 27r/X by m. Then 

 the indi\adual wave trains following the directions of the aforesaid beams 

 are described by the expressions 



A cos {jit — mx cos 4> — my sin <^), A cos {nt — mx cos cp + my sin (p) 



respectively; being added, these give the resultant expression 



A\/2(l + cos 2my sin (p) cos (nt — mx cos) 



which describes a wave motion of which the squared amplitude is given 

 thus: 



(Amplitude) 2 = 2A^{1 -\- cos 2my sin (p) (8) 



and since in all wave theories square of amplitude is taken to be propor- 

 tional to intensity, there is agreement with equation (7), as I remarked. 

 Det ermining the wave-length thus consists in measuring m and equating 

 it to 27r/X. 



All measurements of wave-length are made in essentially this fashion, 

 though the type of diffraction pattern employed varies widely from case 

 to case and is never (except in demonstration experiments) so simple as 

 this example. If anyone speaks of "measuring wave-length" in any 



' The experiment must be performed by separating a single beam of light into two 

 {e.g., by means of a half-silvered and hence semitransparent mirror, or a pair of 

 Fresnel mirrors) and causing the two to recross one another's paths. The fringes are 

 commonly said to constitute an interference pattern, but this is not essentially 

 different from other types of diffraction pattern. 



