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incident wave. Two of the magnetic field components are also found to be zero.

The second set of conclusions relates to the relative amplitudes of the incident, reflected

and transmitted waves. For transmitted and reflected waves we define an amplitudę transmission coefficient xand an amplitudę reflection coefficient pgiven by the equations

where the field quantities to be used are those at the boundary z = 0.

Please notę that it is not true that p+ x= 1. (If you are tempted to entertain this belief, it is worth reflecting upon where such temptation comes from, and whether the

context in which a previously encountered similar relation is valid here).

What is true, and can easly be seen from equations 8.32 and 8.33 to be so, is that X— l+p(8.34)

It is useful to recognise that this equation is not only a valid deduction from equations

8.32 and 8.33, but is also a re-statement of the principle that the tangential component of

electric field is continuous across the boundary, which is in fact the principle from which

equations 8.32 and 8.33 were derived.

The situation we have is completely analogous to the transmission linę problem, if we regard the electric field as analogous to voltage and magnetic field as analogous to

current. To show the connection we define a concept called wave impedance looking in

the +z direction as Z(z) =

Etotal

x

Htotal

(8.35)

For a single travelling piane wave Z(z) = qand is independent of z. When both waves are present the result is morę complicated, and we come to it in a moment. We also define

a reflection coefficient looking in the +z direction P(z) =

E-ixejpz

E+

ixe-jpz (8.36)

This definition is consistent with equation 8.33 above. We can see immediately that p(z) = p(0)ezjpz(8.37)