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Re: dielectric constant



"I also notice a discrepancy between the plots of
n versus w. In Feynman (page 31-8, vol I) n=1
at very law w, which is not true if we identify n
with the square root of the dielectric constant, K."

That's just another mis-print. There is no reason to believe that the
second term (beginning with q^2/(2kappaZero*m) of 31-20, upon which the
authors base the figure, ever becomes zero.

Hecht (fig. 3.14 -- 1st ed.) among many others including even the
ancient Jenkins and White (Fig. 23 I) have it "right". I don't have a
copy of Born and Wolf, but I suspect they have a complete treatment of
this also.

I point out that, as N is complex, in the limit of zero frequency, the
imaginary part ("optical conductivity") is 30 * dc resistance.

"No formula for calculating the first w-zero is given to illustrate the
agreement with experimental data for a particular substance, such as
glass or water."

I haven't taken the time to read Bleaney and Bleaney (E & M) carefully,
but they appear to have done this in general for polar liquids and
compared it to water in the IR.

bc reliving his dissertation research







Ludwik Kowalski wrote:

I would like to thank Jack and Vern for suggesting
good references. Somehow I feel that nobody can
calculate n(w) quantitatively to produce agreement
with experimental data for real substances, such as
those in Figure 3.39 or Table 3.3 (in Hecht). The
idea of resonance frequencies (w-zero) helps to
understand the general shape of the dispersion
curve.

I also notice a discrepancy between the plots of
n versus w. In Feynman (page 31-8, vol I) n=1
at very law w, which is not true if we identify n
with the square root of the dielectric constant, K.
Only in gasses is K very close to unity at w->0.
In Hecht, on the other hand (page 72, 3rd edition)
w=0 corresponds to n=sqr(K). I suppose that his
theoretical formula (3.71) could justify this if
w-zero is properly calculated. No formula for
calculating the first w-zero is given to illustrate
the agreement with experimental data for a
particular substance, such as glass or water.

Without trying to penetrate the derivation I see
that Feynman does make an attempt to compare
expectations with experimental data on sucrose
solutions (table 32-2 on page 32-9, Vol II).
The sum of two numbers from columns G and
H is the experimental result for what is shown
in column F. This refers to lambda=589.3 (Na).
Note, however that column F was also calculated
from the experimental data.
Ludwik Kowalski

Vern Lindberg wrote:

I am puzzled by the fact that the the index of refraction
calculated as the sqr(dielectric_constant) is always
larger, typically by a factor of 2 or 3, than what is
measured in optics. To remove the inconsistency I
would have to assume that the index of refraction
at optical frequencies is much lower than what it is
in electrostatics. Why is it so?
Ludwik Kowalski

Check out the description in Hecht's Optics, (Section 3.3.1 on
Dispersion in the first edition which I have at hand).