

Theory of X-Ray Reflexion, 323 



8. Effect of a Slit. 



This expression, like that for reflexion from one plane, is 

 not general because N may be so large that the reflexion 

 would be greater than the incident beam and the energy 

 would not be conserved. In reality, this would be avoided 

 by the atoms influencing one another's scattering. The 

 -comparison with experiment (§ 14) shows that this is in fact 

 the case, and we must see how. We have so far worked 

 with an unlimited primary beam. Obviously the same 

 result holds if a slit is introduced so broad that it does not 

 cut out any of the radiation near the reflexion angle. The 

 question arises, how narrow may this slit be before the 

 reflexion suffers ? This question may be answered by 

 reference to the figure (p. 317). In front of each of the 



apertures I l9 I 2 in the direction of P, supposed at 



infinite distance, must be introduced a slit. Each slit only 

 has reference to its own aperture and is opaque to the waves 

 from the others. In a direction near P the intensity will be 

 given by the intensity in (3) multiplied by the intensity in 

 this direction corresponding to a single slit. Suppose that 

 the slit is placed symmetrically with regard to the spectral 

 line. For any reasonable values the breadth of the dif- 

 fraction pattern is much greater than that of the maximum 

 in (3). Thus the condition to be satisfied is that the slit is 

 to be of such a width that the intensity has its full value in 

 the central line. Taking roughly the first maximum in a 



k 

 Cornu spiral we find s 2 . — =6, where s is the slit's breadth 



and r its distance from the source. "We can now deduce 

 an upper limit to the reflexion. Taking r- = 30 cm. and 

 £ = 10 9 for medium X rays, we find that all the reflexion 

 occurs within an angular breadth of about 5". If the 

 observed reflexion is more than the whole amount included 

 within 5 /r , it is a sign that the simple theory will not hold, 

 and that in an improved theory which takes account of the 

 influence between atoms, the reflexion must be spread out in 

 a broader pattern than indicated above. 



9. Heterogeneous Radiation, 



The transition from monochromatic radiation to the 

 general " white " radiation is simple. Let the amplitude 

 be represented by 



Y2 



