46 



BELL SYSTEM TECHNICAL JOURNAL 



a reflected field in addition to the original field. This reflected field 

 is produced by an image charge g' = (ei — ei)ql{ei + €2) on the sup- 

 position that the dielectric constant is everywhere equal to €1. Be- 

 low the plane the field is such as would be produced by a charge 

 q" = 2€i5/(ei + €2) if placed where the original charge is, also on the 

 assumption that the dielectric constant is everywhere ei. The 

 charge producing the correct field below the boundary would be 

 g'" = 2€2g/(ei -f ti) if we were to assume €2 as the dielectric constant of 

 the whole space. 



Inspecting equations (7) for an electric current element, which we 

 assume to be perpendicular to the plane interface of two homogeneous 



♦1 



I e -e 



♦ q- 



Fig. 7 



media, we see that the method of images can readily be extended to 

 dynamic fields provided the intrinsic propagation constants of the 

 media are equal. In order to make this conclusion more evident, 

 we replace iun in the first equation by the equivalent product -qa and 

 then calculate the component of E tangential to the interface 



£/ 



(TP-TT I 3 3 \ 



E<,+ COS Q -f E,+ sin Q = rill- — 1 H h ^-, sin cos e. 



It is easy to see that the continuity of the tangential field compo- 

 nents will be preserved if we assume a reflected field on the same side 

 of the boundary and a refracted field on the opposite side in accordance 

 with the following specifications. The reflected field is such as would 

 be produced by an image current element of moment (771 — ri2)Il/{rii -f 772) 



