5.200. (a) a = eEolinw2 =5.10-'6 cm, where E0 = V-2//sac, v =
= aw =_. - 1.7 cm/s; (b) Fm1Fe = 2.9.10-11.
5.201. (a) e = 1 —n0e2/e0mo)2, v = cli1 -4- (noe 2/421280mc2) X2.
5.202. no = (4 n2v2meoie2)(1 ____ n2) ) = 2.4.107 cm-3.
5.203. n — 1 = _noe2x2/8n280mc2 = —5.4.10-7, where no is
the concentration of electrons in carbon.
5.204. (a) x = a cos (wt + (p), where a and q) are defined by
the formulas
a=
eEolm
tan cp — 213w 0,2_4 •
— (092 +41 2(02
Here 13=Ti2m, wo = klm, m is the mass of an electron. (b) (P).
rni3 (eE0/m12 co2
(P)max =__ 4 t; eE no
for 0.)---wo.
5.205. Let us write the wave equation in the form A = A oewot-hx),
where k = 2n/X. If n' = n + ix, then k = (27c/ko)re and
A = Azonxxixoemot-2nnxia.o),
or in the real form
A = Aoei" cos (wt
x),
i.e. the light propagates as a plane wave whose amplitude depends
on x. When x < 0, the amplitude diminishes (the attenuation of
the wave due to absorption). When n' = ix, then
A= AO" cos wt.
This is a standing wave whose amplitude decreases exponentially
(if x < 0). In this case the light experiences total internal reflection
in the medium (without absorption).
5.206. no = 45.c2comc2/e2X;* = 2.0.109 cm-3.
5.208. (a) u = 3/2 v; (b) u
2v; (c) = 1/3 v.
5.209. s= 1+ A/o)2, where A is a constant.
5.210. v = c/n = 1.83.108 m/s, u = El.
(X/n) (dnIc11)1 c/n
= 1.70.108 m/s.
5.211. It is sufficient to discuss three harmonic components of
the train of waves (most easily with the help of a plot).
5.212. I = 1/2/ 0e-4 sin2 cp, where cp = V1H.
5.213. (a) I = / 0 (1 — p)2 (1 + p2
p4
. . .) =
= Jo — 0241 — p 2 ); (b) I = io (1 — 02 6 o.
0.2p2 +0.40+..., )
= 1 0a (1 — 02/(1
0.2 2x ,
p ) where a = exp (—xd).
d2 —d1
1
(1 —p)2N 0.034 cm-1.
5.215. x
IN in
5.216. 'r =(1— p)2 exp [---1/3 (x1 + x2) 11.
(w2— (02)2+ oho ,
in (xi/TO
5.214. x=
=0.35 cm-1.
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