L 668 J 



LXVII. The Diffraction of Waves by a Semi-infinite Screen 

 with a Straight Edge. - By W. G. BlCKLEY, B.Sc, Assis- 

 tant Lecturer in Mathematics, Battersea Polytechnic *. 



§ 1. OINCE Sommerfeld gave the first exact mathematical 

 O solution of the problem of" the diffraction of 

 waves by a semi-infinite screen with a straight edge, 

 several other writers have attempted to obtain the same 

 result by simpler analysis. Some have achieved " sim- 

 plicity " by introducing assumptions not easily justified 

 a priori, while others have used methods which are 

 tantamount to assuming the known form of the solution. 

 It is hoped that the following is free from these defects. 

 It is an extension of the method used by Prof. Lamb | for 

 perpendicular incidence, to the case of oblique incidence. 



§ 2. The problem is, in the first instance, two-dimensional. 

 The trace of the screen will be taken as the positive half of 

 the x axis., The incident waves will be considered to 



Fie-. 1. 



advance in a direction parallel to 10 (fig. 1), and the 

 angle IOX will be denoted by a. Then the incident waves 

 will be given by 



$i = 6 -^ cos «^ si ^'+ c '0 ( Vl 2 -fP)<k = 0, . (1) 



where c is the wave velocity, and /t' = 27r/(wave-]engtl)). 



It will be shown that the boundary conditions can all 

 be satisfied by expressions representing transmitted and 

 reflected waves, 



(h { = ue~ a '^ x cos a ^ y sin a + d) 

 and <f> r = ve -W* cos a-yjAna+ct) respectively, 

 u and v being functions of x and y alone. 



* Communicated by the Author. 



t P. L. M. S. (2) vol. iv. ; ' Hydrodynamics ' (4th ed.) p. 535. 



