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Hulst van de H.C. Light scattering by small particles (Dover Publications, 1981)(K)(600dpi)(T)(480s)(ISBN 0486642283)_P_.djvu |
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Size 18.3Mb Date Jun 30, 2005 |
of incidence t (reversing non-linear scale)...
To derive the amplitude vectors of the total emergent light wave, we must
decompose the emerging vector at each point of the circle into components
with directions parallel to Ax and A2...
In the
central field the "alien" polarization, index 1, is preponderant, except at
the antisolar point itself...
The comple-
complementary colors of the central field and the rings indicate different planes of
polarization, in agreement with Fig...
Ljunggr6n A949) has been more ambitious and has not, a priori, been
content with the approximations that may be obtained from geometrical
optics...
Such measurements have yielded reliable values of n and n' for
numerous materials at a variety of wavelengths...
It can only be
approached by satisfying two conditions:
a. A negligible fraction is reflected, so I m — 1 I <^ 1...
With any method a great number of points have
to be computed before a certain curve, e.g., of Qext as a function of x, can
be drawn...
Full computations of the Mie functions for complex values of m have
been made by several authors...
) have the
coefficients
0 0.30 0.75 1.50 2.65 1.50 0.23
for& = 0 0.1 0.25 0.5 1 2 4
The maximum coefficient, 2.72, is reached for k = 1.23...
It is easily
l~i seen that in this figure w is the area
below the curve B, and the abscissa
of the center of gravity of this area is
An approximate formula for Qab8 found
by analytical integration and useful if
| m | > 2 is given at the end of sec...
They form the transition between the real values m = 1.33
in the visual region and m = 0.9 for very low frequencies...
^A80°) = SaA80°) =
If a particle scatters the light incident on its geometrical cross section
isotropically, its radar cross section equals its geometrical cross section:
a/G = 1...
) and has an amplitude which is, for small values
of xt comparable to the amplitude reflected back from the center of the
exposed surface...
This means that, unless r\ is extremely large, i.e., of the order
of 108 or so, virtually the whole region 3 is characterized by a relatively
large absorption...
Also Jobst's
graph for the absorption by gold
spheres suspended in water at
0.45/* gives a similar result, Qabs =
0.65, at the corresponding refract-
refractive index m = 1.30 — 1.29*
(Table 26)...
By this is meant that it is possible to
define uniquely a function F(z) of the complex variable z (within a certain
area of the complex domain), which has the property that it is regular in
this area and that it equals the given function on the real axis...
Perpendicular Incidence
Perpendicular incidence means that in the preceding equations a = 0,
so I = k and h — 0...
Performing
the integration we obtain
The effective width for extinction, cexti may be defined in a similar
way, but its derivation requires a reasoning analogous to that of sees...
SPECIAL TYPES OF PARTICLES
even simpler: the angles fin and an refer to different physical problems
(case I and case II) and need not appear together in the final formulae...
, it was thought advisable also to find the expressions
of the derivatives of the phase angles in the nodes...
For large values of p the
identical expression 2 + 7rQx(p) was used; Qx(/j) is also found in Jahnke-
Emde...
However,
the slice cut from the Rayleigh scattering pattern is more favorable
in case I than in case II...
More-
Moreover, for this value of m we have
JJy) =Jn(™x) = (-l)-{berBBz) + i beinBz)},
where bern(z) and bein(z) are functions tabulated for use in some engineer-
engineering problems...
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