Abstract

The effective scattering cross sections for metal spheres have been measured through the resonance region, using wavelengths between 0.45 and 15 microns. Spheres of iron and copper sorted into reasonably narrow diameter distributions between 2 and 20 microns were supported in layers on Pliofilm and silver chloride. The results are given in terms of the scattering area coefficient k (the ratio of scattering cross section to projected area of the spheres) as a function of α (the ratio of sphere circumference to the wavelength used). These results are in general accord with qualitative predictions based on the Mie theory. Detail in the resonance region is obscured by the finite diameter distributions of the samples.

© 1952 Optical Society of America

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References

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  1. G. Mie, Ann. Physik 25, 277 (1908).
  2. J. A. Stratton, Electromagnetic Theory (McGraw-Hill Book Company, Inc., New York, 1944).
  3. Rayleigh, Phil. Mag. 41, 447 (1871); Phil Mag. 12, 81 (1881).
  4. J. A. Stratton and H. G. Houghton, Phys. Rev. 36, 159 (1931).
    [CrossRef]
  5. H. G. Houghton and W. R. Chalker, J. Opt. Soc. Am. 39, 955 (1949).
    [CrossRef]
  6. V. K. LaMer, J. Phys. and Colloid Chem. 52, 65 (1948).
    [CrossRef]
  7. D. Sinclair, J. Opt. Soc. Am. 37, 475 (1947).
    [CrossRef] [PubMed]
  8. A. N. Lowan, Tables of Scattering Functions for Spherical Particles (National Bureau of Standards, Applied Mathematics Series 4, 1949).
  9. M. D. Barnes and V. K. LaMer, J. Colloid Sci. 1, 71, 79 (1946).
    [CrossRef]
  10. Barnes, Kenyon, Zeiser, and LaMer, J. Colloid Sci. 2, 257 (1947).
    [CrossRef]
  11. A. J. F. Siegert, Radar System Engineering (McGraw-Hill Book Company, Inc., New York, 1947), MIT Radiation Laboratory Series 1, pp. 63–65.
  12. P. J. Rubenstein, , April, 1943.
  13. A. L. Aden, J. Appl. Phys. 22, 601–605 (1951).
    [CrossRef]
  14. L. Brillouin, J. Appl. Phys. 20, 1110 (1949).
    [CrossRef]
  15. P. S. Roller, (1931); Proc. A.S.T.M. 32, 607 (1932); J. Am. Ceramic Soc. 20, 167 (1937).

1951 (1)

A. L. Aden, J. Appl. Phys. 22, 601–605 (1951).
[CrossRef]

1949 (2)

1948 (1)

V. K. LaMer, J. Phys. and Colloid Chem. 52, 65 (1948).
[CrossRef]

1947 (2)

D. Sinclair, J. Opt. Soc. Am. 37, 475 (1947).
[CrossRef] [PubMed]

Barnes, Kenyon, Zeiser, and LaMer, J. Colloid Sci. 2, 257 (1947).
[CrossRef]

1946 (1)

M. D. Barnes and V. K. LaMer, J. Colloid Sci. 1, 71, 79 (1946).
[CrossRef]

1931 (1)

J. A. Stratton and H. G. Houghton, Phys. Rev. 36, 159 (1931).
[CrossRef]

1908 (1)

G. Mie, Ann. Physik 25, 277 (1908).

1871 (1)

Rayleigh, Phil. Mag. 41, 447 (1871); Phil Mag. 12, 81 (1881).

Aden, A. L.

A. L. Aden, J. Appl. Phys. 22, 601–605 (1951).
[CrossRef]

Barnes,

Barnes, Kenyon, Zeiser, and LaMer, J. Colloid Sci. 2, 257 (1947).
[CrossRef]

Barnes, M. D.

M. D. Barnes and V. K. LaMer, J. Colloid Sci. 1, 71, 79 (1946).
[CrossRef]

Brillouin, L.

L. Brillouin, J. Appl. Phys. 20, 1110 (1949).
[CrossRef]

Chalker, W. R.

Houghton, H. G.

H. G. Houghton and W. R. Chalker, J. Opt. Soc. Am. 39, 955 (1949).
[CrossRef]

J. A. Stratton and H. G. Houghton, Phys. Rev. 36, 159 (1931).
[CrossRef]

Kenyon,

Barnes, Kenyon, Zeiser, and LaMer, J. Colloid Sci. 2, 257 (1947).
[CrossRef]

LaMer,

Barnes, Kenyon, Zeiser, and LaMer, J. Colloid Sci. 2, 257 (1947).
[CrossRef]

LaMer, V. K.

V. K. LaMer, J. Phys. and Colloid Chem. 52, 65 (1948).
[CrossRef]

M. D. Barnes and V. K. LaMer, J. Colloid Sci. 1, 71, 79 (1946).
[CrossRef]

Lowan, A. N.

A. N. Lowan, Tables of Scattering Functions for Spherical Particles (National Bureau of Standards, Applied Mathematics Series 4, 1949).

Mie, G.

G. Mie, Ann. Physik 25, 277 (1908).

Rayleigh,

Rayleigh, Phil. Mag. 41, 447 (1871); Phil Mag. 12, 81 (1881).

Roller, P. S.

P. S. Roller, (1931); Proc. A.S.T.M. 32, 607 (1932); J. Am. Ceramic Soc. 20, 167 (1937).

Rubenstein, P. J.

P. J. Rubenstein, , April, 1943.

Siegert, A. J. F.

A. J. F. Siegert, Radar System Engineering (McGraw-Hill Book Company, Inc., New York, 1947), MIT Radiation Laboratory Series 1, pp. 63–65.

Sinclair, D.

Stratton, J. A.

J. A. Stratton and H. G. Houghton, Phys. Rev. 36, 159 (1931).
[CrossRef]

J. A. Stratton, Electromagnetic Theory (McGraw-Hill Book Company, Inc., New York, 1944).

Zeiser,

Barnes, Kenyon, Zeiser, and LaMer, J. Colloid Sci. 2, 257 (1947).
[CrossRef]

Ann. Physik (1)

G. Mie, Ann. Physik 25, 277 (1908).

J. Appl. Phys. (2)

A. L. Aden, J. Appl. Phys. 22, 601–605 (1951).
[CrossRef]

L. Brillouin, J. Appl. Phys. 20, 1110 (1949).
[CrossRef]

J. Colloid Sci. (2)

M. D. Barnes and V. K. LaMer, J. Colloid Sci. 1, 71, 79 (1946).
[CrossRef]

Barnes, Kenyon, Zeiser, and LaMer, J. Colloid Sci. 2, 257 (1947).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Phys. and Colloid Chem. (1)

V. K. LaMer, J. Phys. and Colloid Chem. 52, 65 (1948).
[CrossRef]

Phil. Mag. (1)

Rayleigh, Phil. Mag. 41, 447 (1871); Phil Mag. 12, 81 (1881).

Phys. Rev. (1)

J. A. Stratton and H. G. Houghton, Phys. Rev. 36, 159 (1931).
[CrossRef]

Other (5)

J. A. Stratton, Electromagnetic Theory (McGraw-Hill Book Company, Inc., New York, 1944).

A. N. Lowan, Tables of Scattering Functions for Spherical Particles (National Bureau of Standards, Applied Mathematics Series 4, 1949).

A. J. F. Siegert, Radar System Engineering (McGraw-Hill Book Company, Inc., New York, 1947), MIT Radiation Laboratory Series 1, pp. 63–65.

P. J. Rubenstein, , April, 1943.

P. S. Roller, (1931); Proc. A.S.T.M. 32, 607 (1932); J. Am. Ceramic Soc. 20, 167 (1937).

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Figures (4)

Fig. 1
Fig. 1

Qualitative k-vs-α curve for a metal sphere.

Fig. 2
Fig. 2

Schemes used in distributing spheres over supporting surfaces.

Fig. 3
Fig. 3

Diameter distribution for sample B. Area average diameter is 2.71 microns.

Fig. 4
Fig. 4

Experimental k-vs-α curve for iron and copper spheres.

Tables (1)

Tables Icon

Table I Summary of sample data.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

d I / I = - k π a 2 N d l ,
T = I / I 0 = exp ( - k π a 2 N l ) ,
Δ I / I 0 = ( I 1 - I 0 ) / I 0 = T 1 - 1 = - k π a 2 n
I / I 0 = T = ( 1 - k π a 2 n ) ν .
n = ( 1 - T 1 / ν ) / π a 2 k .