TABLE OF CONTENTS The purpose in going from a first order to a second order boundary condition is to improve the accuracy. We now consider a few simple but important cases to show how the coefficients can be determined and examine the accuracy that can be achieved.
We take first a thin layer consisting of a homogeneous dielectric whose permittivity and permeability are ? = ? r ? 0 and ? = ? r ? 0 respectively, occupying the region 
, - ? <, x, z < ?, with free space surrounding the layer. It is assumed that the dielectric provides a low contrast, so that ? rand ? r are not large compared with unity. As illustrated in Fig. 5-1, we seek to represent the effect of the layer using a current sheet in the plane y = ? where 
.
Following Weinstein (1969) the tangential electric field components within the layer are expanded in Taylor series in y. Thus
where the prime denotes the internal field and we show only the dependence on the y coordinate perpendicular to the layer. By using the exact boundary conditions at y = 
we can write this in terms of the external fields as
and a further expansion of the external fields enables us to express the right hand side in...
