(Reductions) When a typical case [Matv, p.122, (16.2)] can represent the general case [Hec,
p.111, (4.12), (4.13), and (4.14)] we must explain why the discussion of the
typical will not lose the generality. First, note that
er
and et
are independent of r on the interface. Then by comparing [Hec, p.112, Fig. 4.38]
with [Matv, p.123, Fig. 58], we see that if we had chosen the origin to be in
the interface, er
and et
would have been zero [Hec, p.113, l.c., l.2]. [Matv, Sec. 16] lacks this important
justification.
(Assumptions must be clarified and justifiable) [Wangs, p.411, l.-12]
just assumes the directions of Ei^, Er^,
and Et^ by brute force
in one case and vaguely describes their directions in the other case.
In contrast, [Hec, p.113, l.c., l.-11-l.-9] gives a more subtle reason why we may do
so. In addition, [Hec, p.117, r.c., l.7-l.10] clarifies the meaning of phase shift
by defining carefully what in-phase and out-of-phase mean.
Remark. If we trace the definition given in [Hec, p.117, r.c., l.7-l.10] to its
root, we see that it is the consequence of the convention given in [Born,
p.37, l.-12-l.-11].
(Derivations) [Matv, p.131, (16.43a)] is valid if
ni<
nt or if (ni> nt
and qin< qlim)
even though the proof is based on the former case [Matv, p.129, Fig. 65]. The same proof is also valid
for the latter case. The formula for the the later case has an application in [Hec,
p.663, lc, l.-5]. Another example is given by [Matv,
p.129, (16.33c)]. The formula for the case (ni> nt
and qin< qlim)
has an application in [Hec, p.117, l.c., l.-5].