Abstract

Total scattering coefficients for concentric spheres with inner sphere <i>m</i><sub>1</sub>=2.1050 and concentric spherical shell <i>m</i><sub>2</sub>=1.4821 have been computed for ν=2π<i>b</i>/λ over the interval 0.1 (.1) 23.0 (2) 53.0 and for α/ν values of 0, 0.2, 0.4, 0.6, 0.8, 0.9, 0.95, 0.98, 0.99, and 1.00, where α=2πα/λ, <i>a</i> and <i>b</i> are the radii of the inner and total spheres, and λ is the wavelength. The results are compared with those obtained by a small particle approximation, the approximation suggested by Ryde, the Rayleigh-Gans method and an approximation based on using the single sphere method with a volume averaged refractive index. The Rayleigh-Gans equations for concentric spheres are derived. The small particle approximation permits accurate estimation of the total scattering coefficient for any combination of α and ν up to ν=1.4.

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  1. A. L. Aden and M. Kerker, J. Appl. Phys. 22, 1242 (1951).
  2. M. Kerker, P. Langleben, and K. L. S. Gunn, J. Meteorol. 8, 424 (1951).
  3. D. Atlas, M. Kerker, and W. Hitschfeld, J. Atm. Terrest. Phys. 3, 108 (1953).
  4. B. M. Herman and L. J. Battan, Institute of Atmospheric Physics, University of Arizona, Tucson, Arizona, 1960, Scientific Report No. 15 (unpublished).
  5. D. Atlas, W. G. Harper, F. H. Ludlam, and W. C. Macklin, Quart. J. Roy. Meteorol. Soc. 86, 468 (1960).
  6. P. Debye and L. K. H. van Beek, J. Chem. Phys. 31, 1595 (1959).
  7. H. Oser (private communication).
  8. E. Matijević, M. Kerker, and K. F. Schulz, Discussions Faraday Soc. 30, 178, 223 (1960).
  9. E. Matijević, K. F. Schulz, and M. Kerker, J. Colloid Sci. 17, 26 (1962).
  10. J. L. Greenstein, "Polarization of Starlight by the Interstellar Medium," Lowell Obs. Bull. No. 5, IV, No. 17 (1960).
  11. A. N. Lowan, "Tables of Scattering Functions for Spherical Particles," National Bureau of Standards, Applied Mathematics Series 4, U. S. Government Printing Office, Washington (1948).
  12. R. O. Gumprecht and C. M. Sliepcevich, Tables of Light Scattering Functions for Spherical Particles (University of Michigan Ann Arbor, Michigan, 1951).
  13. H. C. Van de Hulst, Recherches Astron. Obs. d'Utrecht 11, (1946).
  14. H. C. Van de Hulst, Light Scattering by Small Particles (John Wiley & Sons, Inc., New York, 1957).
  15. P. G. W. Hawksley, Bull. Brit. Coal Utilization Research Assoc. 16, 117, 181 (1952).
  16. R. B. Penndorf, "New Tables of Mie Scattering Functions for Spherical Particles. Part 6: Total Mie Scattering Coefficients for Real Refractive Indices." Geophysical Research Papers No. 45, A. F. Cambridge Research Center, Bedford, Massachusetts, March, 1956. Parts of this apear in J. Meteorol. 13, 219 (1956); J. Opt. Soc. Am. 46, 1001 (1956); ibid. 47, 603, 1010 (1957); J. Phys. Chem. 62, 1537 (1958).
  17. M. Kerker, J. P. Kratohvil and E. Matijević, J. Phys. Chem. 65, 1713 (1961).
  18. A. Güttler, Ann. Physik 11, 65 (1952).
  19. J. W. Ryde, Meteorological Factors in Radio-Wave Propagation (The Physical Society, London, 1946), pp. 169–188.
  20. Lord Rayleigh, Proc. Roy. Soc. (London) A90, 219 (1914).
  21. J. W. Ryde and B. S. Cooper, Proc. Roy. Soc. (London) A131, 1461 (1931).
  22. Reference 14, p. 90.

1960 (1)

J. L. Greenstein, "Polarization of Starlight by the Interstellar Medium," Lowell Obs. Bull. No. 5, IV, No. 17 (1960).

Aden, A. L.

A. L. Aden and M. Kerker, J. Appl. Phys. 22, 1242 (1951).

Atlas, D.

D. Atlas, M. Kerker, and W. Hitschfeld, J. Atm. Terrest. Phys. 3, 108 (1953).

D. Atlas, W. G. Harper, F. H. Ludlam, and W. C. Macklin, Quart. J. Roy. Meteorol. Soc. 86, 468 (1960).

Battan, L. J.

B. M. Herman and L. J. Battan, Institute of Atmospheric Physics, University of Arizona, Tucson, Arizona, 1960, Scientific Report No. 15 (unpublished).

Cooper, B. S.

J. W. Ryde and B. S. Cooper, Proc. Roy. Soc. (London) A131, 1461 (1931).

Debye, P.

P. Debye and L. K. H. van Beek, J. Chem. Phys. 31, 1595 (1959).

Greenstein, J. L.

J. L. Greenstein, "Polarization of Starlight by the Interstellar Medium," Lowell Obs. Bull. No. 5, IV, No. 17 (1960).

Gumprecht, R. O.

R. O. Gumprecht and C. M. Sliepcevich, Tables of Light Scattering Functions for Spherical Particles (University of Michigan Ann Arbor, Michigan, 1951).

Gunn, K. L. S.

M. Kerker, P. Langleben, and K. L. S. Gunn, J. Meteorol. 8, 424 (1951).

Güttler, A.

A. Güttler, Ann. Physik 11, 65 (1952).

Harper, W. G.

D. Atlas, W. G. Harper, F. H. Ludlam, and W. C. Macklin, Quart. J. Roy. Meteorol. Soc. 86, 468 (1960).

Hawksley, P. G. W.

P. G. W. Hawksley, Bull. Brit. Coal Utilization Research Assoc. 16, 117, 181 (1952).

Herman, B. M.

B. M. Herman and L. J. Battan, Institute of Atmospheric Physics, University of Arizona, Tucson, Arizona, 1960, Scientific Report No. 15 (unpublished).

Hitschfeld, W.

D. Atlas, M. Kerker, and W. Hitschfeld, J. Atm. Terrest. Phys. 3, 108 (1953).

Kerker, M.

D. Atlas, M. Kerker, and W. Hitschfeld, J. Atm. Terrest. Phys. 3, 108 (1953).

A. L. Aden and M. Kerker, J. Appl. Phys. 22, 1242 (1951).

M. Kerker, P. Langleben, and K. L. S. Gunn, J. Meteorol. 8, 424 (1951).

M. Kerker, J. P. Kratohvil and E. Matijević, J. Phys. Chem. 65, 1713 (1961).

E. Matijević, M. Kerker, and K. F. Schulz, Discussions Faraday Soc. 30, 178, 223 (1960).

E. Matijević, K. F. Schulz, and M. Kerker, J. Colloid Sci. 17, 26 (1962).

Kratohvil, J. P.

M. Kerker, J. P. Kratohvil and E. Matijević, J. Phys. Chem. 65, 1713 (1961).

Langleben, P.

M. Kerker, P. Langleben, and K. L. S. Gunn, J. Meteorol. 8, 424 (1951).

Lowan, A. N.

A. N. Lowan, "Tables of Scattering Functions for Spherical Particles," National Bureau of Standards, Applied Mathematics Series 4, U. S. Government Printing Office, Washington (1948).

Ludlam, F. H.

D. Atlas, W. G. Harper, F. H. Ludlam, and W. C. Macklin, Quart. J. Roy. Meteorol. Soc. 86, 468 (1960).

Macklin, W. C.

D. Atlas, W. G. Harper, F. H. Ludlam, and W. C. Macklin, Quart. J. Roy. Meteorol. Soc. 86, 468 (1960).

Matijevic, E.

E. Matijević, K. F. Schulz, and M. Kerker, J. Colloid Sci. 17, 26 (1962).

E. Matijević, M. Kerker, and K. F. Schulz, Discussions Faraday Soc. 30, 178, 223 (1960).

M. Kerker, J. P. Kratohvil and E. Matijević, J. Phys. Chem. 65, 1713 (1961).

Oser, H.

H. Oser (private communication).

Penndorf, R. B.

R. B. Penndorf, "New Tables of Mie Scattering Functions for Spherical Particles. Part 6: Total Mie Scattering Coefficients for Real Refractive Indices." Geophysical Research Papers No. 45, A. F. Cambridge Research Center, Bedford, Massachusetts, March, 1956. Parts of this apear in J. Meteorol. 13, 219 (1956); J. Opt. Soc. Am. 46, 1001 (1956); ibid. 47, 603, 1010 (1957); J. Phys. Chem. 62, 1537 (1958).

Rayleigh, Lord

Lord Rayleigh, Proc. Roy. Soc. (London) A90, 219 (1914).

Ryde, J. W.

J. W. Ryde and B. S. Cooper, Proc. Roy. Soc. (London) A131, 1461 (1931).

J. W. Ryde, Meteorological Factors in Radio-Wave Propagation (The Physical Society, London, 1946), pp. 169–188.

Schulz, K. F.

E. Matijević, M. Kerker, and K. F. Schulz, Discussions Faraday Soc. 30, 178, 223 (1960).

E. Matijević, K. F. Schulz, and M. Kerker, J. Colloid Sci. 17, 26 (1962).

Sliepcevich, C. M.

R. O. Gumprecht and C. M. Sliepcevich, Tables of Light Scattering Functions for Spherical Particles (University of Michigan Ann Arbor, Michigan, 1951).

van Beek, L. K. H.

P. Debye and L. K. H. van Beek, J. Chem. Phys. 31, 1595 (1959).

Van de Hulst, H. C.

H. C. Van de Hulst, Recherches Astron. Obs. d'Utrecht 11, (1946).

H. C. Van de Hulst, Light Scattering by Small Particles (John Wiley & Sons, Inc., New York, 1957).

Lowell Obs. Bull. No. 5 (1)

J. L. Greenstein, "Polarization of Starlight by the Interstellar Medium," Lowell Obs. Bull. No. 5, IV, No. 17 (1960).

Other (21)

A. N. Lowan, "Tables of Scattering Functions for Spherical Particles," National Bureau of Standards, Applied Mathematics Series 4, U. S. Government Printing Office, Washington (1948).

R. O. Gumprecht and C. M. Sliepcevich, Tables of Light Scattering Functions for Spherical Particles (University of Michigan Ann Arbor, Michigan, 1951).

H. C. Van de Hulst, Recherches Astron. Obs. d'Utrecht 11, (1946).

H. C. Van de Hulst, Light Scattering by Small Particles (John Wiley & Sons, Inc., New York, 1957).

P. G. W. Hawksley, Bull. Brit. Coal Utilization Research Assoc. 16, 117, 181 (1952).

R. B. Penndorf, "New Tables of Mie Scattering Functions for Spherical Particles. Part 6: Total Mie Scattering Coefficients for Real Refractive Indices." Geophysical Research Papers No. 45, A. F. Cambridge Research Center, Bedford, Massachusetts, March, 1956. Parts of this apear in J. Meteorol. 13, 219 (1956); J. Opt. Soc. Am. 46, 1001 (1956); ibid. 47, 603, 1010 (1957); J. Phys. Chem. 62, 1537 (1958).

M. Kerker, J. P. Kratohvil and E. Matijević, J. Phys. Chem. 65, 1713 (1961).

A. Güttler, Ann. Physik 11, 65 (1952).

J. W. Ryde, Meteorological Factors in Radio-Wave Propagation (The Physical Society, London, 1946), pp. 169–188.

Lord Rayleigh, Proc. Roy. Soc. (London) A90, 219 (1914).

J. W. Ryde and B. S. Cooper, Proc. Roy. Soc. (London) A131, 1461 (1931).

Reference 14, p. 90.

A. L. Aden and M. Kerker, J. Appl. Phys. 22, 1242 (1951).

M. Kerker, P. Langleben, and K. L. S. Gunn, J. Meteorol. 8, 424 (1951).

D. Atlas, M. Kerker, and W. Hitschfeld, J. Atm. Terrest. Phys. 3, 108 (1953).

B. M. Herman and L. J. Battan, Institute of Atmospheric Physics, University of Arizona, Tucson, Arizona, 1960, Scientific Report No. 15 (unpublished).

D. Atlas, W. G. Harper, F. H. Ludlam, and W. C. Macklin, Quart. J. Roy. Meteorol. Soc. 86, 468 (1960).

P. Debye and L. K. H. van Beek, J. Chem. Phys. 31, 1595 (1959).

H. Oser (private communication).

E. Matijević, M. Kerker, and K. F. Schulz, Discussions Faraday Soc. 30, 178, 223 (1960).

E. Matijević, K. F. Schulz, and M. Kerker, J. Colloid Sci. 17, 26 (1962).

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