
226 OPTICS FOR ENGINEERS
where
E
i
is the incident eld
E
r
is the reected eld
E
t
is the transmitted eld
Likewise, for the magnetic eld,
H
A
= H
i
−H
r
H
D
= H
t
, (7.144)
where the negative sign on the reected component is to maintain a right-handed coordinate
system upon reection.
The boundary conditions on H can be expressed in terms of E as
E
B
nZ
0
=
E
A
n
0
Z
0
E
c
nZ
0
=
E
D
n
t
Z
0
using Equation 1.40, or, multiplying by Z
0
,
E
B
n
=
E
A
n
0
E
C
n
=
E
D
n
t
. (7.145)
The eld inside the material consists of a wave propagating to the right,
E
right
e
inkz
and H
right
e
inkz
=
1
nZ
0
E
right
e
inkz
(7.146)
and one propagating to the left
E
left
e
−inkz
and H
left
e
−inkz
=−
1
nZ
0
E
left
e
−inkz
. (7.147)
At the boundaries,
E
B
=