8 BIOLOGICAL EFFECTS OF RADIATION 



The relation {1) between wave-length of waves and momentum of 

 corpuscles is therefore one which we are obhged to accept if we wish to 

 use both the wave picture and the corpuscle picture of light. 



The relation {2) may be derived from {!) by means of a classical 

 theorem concerning the ratio between the energy-density of a beam of 

 light and the pressure which the beam exerts upon an object on which 

 it falls. Conceive a stream of radiation in the form of an extremely 

 long train of plane waves, flowing against a blackened plate faced nor- 

 mally against the direction in which they advance, which totally absorbs 

 them. Say that the beam has intensity 7, which means that an amount 

 of energy / appears, in the form of heat, in unit area of the blackened 

 plate in unit time. The light exerts a pressure, say P, against the plate; 

 this means that unit area of the plate acquires in unit time an amount of 

 momentum P. The classical undulatory theory predicts that P should 

 be equal to the quotient of I by c, and this is confirmed by experience. 

 Now / is equal to the product of E, the energy of a photon, by A^, the 

 number of photons which strike the plate in unit time; while P is equal 

 to the product of p, the momentum of a photon, by the same number N. 

 Hence E must be equal to pc, and this statement is none other than 

 equation {2). 



Equations {!) and {2) may also be proved jointly valid by invoking 

 the Compton effect, and equation {2) by itself may be proved vaHd by 

 invoking the external photoelectric effect of metals, both of which will 

 be treated in later sections of this article. Before going further, however, 

 we should consider more closely how the undulatory theory is tested 

 and how wave-length is determined. 



MONOCHROMATIC LIGHT AND MEASUREMENT OF WAVE-LENGTH 

 As Newton found in his classical experiments in optics, a narrow beam 

 of white light is converted by a prism into a diverging beam of which the 

 color varies from one side to the other of the beam, but if a sufficiently 

 narrow portion of this divergent beam is isolated (by means of a slit 

 in an opaque screen) and sent through a second prism, it is neither 

 broadened nor changed in color. Light of the latter character is called 

 monochromatic and has the power of forming diffraction patterns indicat- 

 ing a single wave-length. Every "measurement" of a wave-length is an 

 observation on a diffraction pattern. Owing to the importance of this 

 matter I will develop the simplest case. 



Imagine two beams of identical monochromatic light moving parallel 

 to the x2/-plane, one making an angle ip and the other an angle - ^ with 

 the X-axis, so that they make an angle 2<^ with each other. Were they 

 purely corpuscular, they would cross each other without interference. 

 (The reader may object that corpuscles of the two beams would collide 



