Irodov – Problems in General Physics

5.200. (a) a = eEolinw 2 =5.10-' 6 cm, where E 0 = V-2//sac, v =

= aw =_.- 1.7 cm/s; (b) Fm1Fe = 2.9.10-11.

5.201. (a) e = 1 —n 0 e 2 /e 0 mo) 2 , v = cli1 -4- (noe2/4^212 80mc2) X2.

5.202. no = (4n^2 v^2 meoie2)(1 ____ n 2 ) ) = 2.4.10 7 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 •

— (09^2 +^412 (0^2

Here 13=Ti2m, wo = klm, m is the mass of an electron. (b) (P).
rni3 (eE0/m1^2 co2^ (P)max =__^4 t; eEno^ 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;* = 2.0.10^9 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 = 1.83.10^8 m/s, u = El.^ (X/n) (dnIc11)1 c/n
= 1.70.10 8 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 / 0 e-4 sin 2 cp, where cp = V1H.
5.213. (a) I = / 0 (1 — p) 2 (1 + p 2 p 4.. .) =
= Jo — 0 241 — p^2 ); (b) I = io ( 1 — 02^6
o. 0 .2 p 2 +0.40+..., )^
= 1 0 a (1 — 02/(1^0 .2 2x , p ) where a = exp (—xd).
d 2 —d1
1 (1 —p)2N 0.034 cm-1.
5.215. x IN in
5.216. 'r =(1—p) 2 exp [--- (^1) /3 (x1 + x 2 ) 11.
(w2— (02)2+ oho ,
in (xi /TO
5.214. x= =0.35 cm-1.
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