Abstract

<p>The tristimulus color system is used to describe the colors of the light scattered by spheres with radii <i>a</i>=0.2, 0.3, 0.4, 0.5, 0.6, 0.8, 1.0, and 1.2 µ for real refractive indices <i>m</i>= 1.31 and 1.46 and by spheres with radii <i>a</i>=0.1, 0.2, O.4 µ for complex refractive index corresponding to a highly absorbing substance such as vanadium pentoxide. The quantities calculated are the dominant wavelength, purity, the visible intensity, and the intensity for unpolarized incident white light from a 3200° K source as well as for each of the two plane-polarized components.</p><p>The angular variation of colors designated as higher-order Tyndall spectra (H.O.T.S.) occurs only for radii comparable to the wavelength. For small particles, the light is blue, corresponding to Rayleigh scattering, while for radii <i>a</i>>0.8 µ, the scattered light is uniformly yellow. At intermediate sizes 0.2µ≤<i>a</i>≤0.8µ the H.O.T.S. described by Sinclair and La Mer occur. However, there is no correlation between the appearance of the color bands and the intensity peaks of the scattered light. It is possible to have a polydisperse system in the intermediate size range exhibit H.O.T.S. while a perfectly monodisperse system of larger radius does not exhibit this phenomenon. A visual measure of the polarization ratio at two or three backward directions can serve to determine the particle size.</p>

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  1. Lord Rayleigh, Phil. Mag. 41, 107, 274, 447 (1871); Scientific Papers (Dover Publications, Inc., New York, 1964) Vol., I, pp. 87–110.
  2. G. Mie, Ann. Physik 25, 377 (1908).
  3. L. Lorenz, Vidensk. Selsk. Skr. 6, (1890); Oeures Scientifique (Copenhagen, 1898), Vol. I, p. 405; A. E. H. Love, Proc. London Math. Soc. 30, 308 (1899); P. Debye, Ann. Physik 30, 57 (1909); J. W. Nicholson, Proc. London Math. Soc. 9, 67 (1910); 11, 277 (1912); T. S. Bromwich, Phil. Mag. 38, 144 (1919).
  4. M. Kerker, editor, Electromagnetic Scattering (Pergamon Press, New York, 1963).
  5. R. H. Doremus, J. Chem. Phys. 40, 2389 (1964); 42, 414 (1965).
  6. D. Sinclair and V. K. La Mer, Chem. Revs. 44, 249 (1949).
  7. I. Johnson and V. K. La Mer, J. Am. Chem. Soc. 69, 1184 (1947).
  8. M. Kerker, E. Daby, G. L. Cohen, J. P. Kratohvil, and E. Matijević, J. Phys. Chem. 67, 2105 (1963).
  9. H. C. van de Hulst, Light Scattering by Small Parlicles (John Wiley & Sons, New York, 1957).
  10. Committee on Colorimetry of the Optical Society of America, The Science of Color (Optical Society of America, Washington, D. C., 1963).
  11. J. E. McCarley, C. E. Green, and K. H. Horowitz, J. Opt. Soc. Am. 55, 355 (1965).
  12. R. T. Jacobsen, Ph.D. thesis, Clarkson College of Technology, Potsdam, New York, 1966.
  13. Deposited as Document number 8954 with the ADI Auxiliary Publications Project, Photoduplication Service, Library of Congress, Washington 25, D. C. A copy may be secured by citing the Document number and by remitting $12.50 for photoprints, or $4.25 for 35 mm microfilm. Advance payment is required. Make checks or money orders payable to: Chief, Photoduplication Service, Library of Congress.
  14. B. Ray, Proc. Indian Assoc. Cultiv. Sci. 7, 1 (1921).
  15. M. Kerker, W. A. Farone, and W. F. Espenscheid, J. Colloid. Interface Sci. 21, 459 (1966).
  16. W. F. Espenscheid, M. Kerker, and E. Matijević, J. Phys. Chem. 68, 3093 (1964).
  17. M. Kerker and V. K. La Mer, J. Am. Chem. Soc. 72, 3516 (1950).
  18. M. Kerker, E. Matijević, W. F. Espenscheid, W. A. Farone, and S. Kitani, J. Colloid. Sci. 19, 213 (1964).
  19. W. F. Espenscheid, E. Willis, E. Matijević, and M. Kerker, J. Colloid. Sci. 20, 501 (1965).
  20. A. C. Hardy and F. H. Perrin, The Principles of Optics (McGraw-Hill Book Co., New York, 1932).

1966

R. T. Jacobsen, Ph.D. thesis, Clarkson College of Technology, Potsdam, New York, 1966.

M. Kerker, W. A. Farone, and W. F. Espenscheid, J. Colloid. Interface Sci. 21, 459 (1966).

1965

J. E. McCarley, C. E. Green, and K. H. Horowitz, J. Opt. Soc. Am. 55, 355 (1965).

W. F. Espenscheid, E. Willis, E. Matijević, and M. Kerker, J. Colloid. Sci. 20, 501 (1965).

1964

M. Kerker, E. Matijević, W. F. Espenscheid, W. A. Farone, and S. Kitani, J. Colloid. Sci. 19, 213 (1964).

W. F. Espenscheid, M. Kerker, and E. Matijević, J. Phys. Chem. 68, 3093 (1964).

R. H. Doremus, J. Chem. Phys. 40, 2389 (1964); 42, 414 (1965).

1963

M. Kerker, E. Daby, G. L. Cohen, J. P. Kratohvil, and E. Matijević, J. Phys. Chem. 67, 2105 (1963).

1950

M. Kerker and V. K. La Mer, J. Am. Chem. Soc. 72, 3516 (1950).

1949

D. Sinclair and V. K. La Mer, Chem. Revs. 44, 249 (1949).

1947

I. Johnson and V. K. La Mer, J. Am. Chem. Soc. 69, 1184 (1947).

1921

B. Ray, Proc. Indian Assoc. Cultiv. Sci. 7, 1 (1921).

1908

G. Mie, Ann. Physik 25, 377 (1908).

1890

L. Lorenz, Vidensk. Selsk. Skr. 6, (1890); Oeures Scientifique (Copenhagen, 1898), Vol. I, p. 405; A. E. H. Love, Proc. London Math. Soc. 30, 308 (1899); P. Debye, Ann. Physik 30, 57 (1909); J. W. Nicholson, Proc. London Math. Soc. 9, 67 (1910); 11, 277 (1912); T. S. Bromwich, Phil. Mag. 38, 144 (1919).

1871

Lord Rayleigh, Phil. Mag. 41, 107, 274, 447 (1871); Scientific Papers (Dover Publications, Inc., New York, 1964) Vol., I, pp. 87–110.

Cohen, G. L.

M. Kerker, E. Daby, G. L. Cohen, J. P. Kratohvil, and E. Matijević, J. Phys. Chem. 67, 2105 (1963).

Daby, E.

M. Kerker, E. Daby, G. L. Cohen, J. P. Kratohvil, and E. Matijević, J. Phys. Chem. 67, 2105 (1963).

Doremus, R. H.

R. H. Doremus, J. Chem. Phys. 40, 2389 (1964); 42, 414 (1965).

Espenscheid, W. F.

M. Kerker, W. A. Farone, and W. F. Espenscheid, J. Colloid. Interface Sci. 21, 459 (1966).

W. F. Espenscheid, E. Willis, E. Matijević, and M. Kerker, J. Colloid. Sci. 20, 501 (1965).

M. Kerker, E. Matijević, W. F. Espenscheid, W. A. Farone, and S. Kitani, J. Colloid. Sci. 19, 213 (1964).

W. F. Espenscheid, M. Kerker, and E. Matijević, J. Phys. Chem. 68, 3093 (1964).

Farone, W. A.

M. Kerker, W. A. Farone, and W. F. Espenscheid, J. Colloid. Interface Sci. 21, 459 (1966).

M. Kerker, E. Matijević, W. F. Espenscheid, W. A. Farone, and S. Kitani, J. Colloid. Sci. 19, 213 (1964).

Green, C. E.

J. E. McCarley, C. E. Green, and K. H. Horowitz, J. Opt. Soc. Am. 55, 355 (1965).

Hardy, A. C.

A. C. Hardy and F. H. Perrin, The Principles of Optics (McGraw-Hill Book Co., New York, 1932).

Horowitz, K. H.

J. E. McCarley, C. E. Green, and K. H. Horowitz, J. Opt. Soc. Am. 55, 355 (1965).

Jacobsen, R. T.

R. T. Jacobsen, Ph.D. thesis, Clarkson College of Technology, Potsdam, New York, 1966.

Johnson, I.

I. Johnson and V. K. La Mer, J. Am. Chem. Soc. 69, 1184 (1947).

Kerker, M.

M. Kerker, W. A. Farone, and W. F. Espenscheid, J. Colloid. Interface Sci. 21, 459 (1966).

W. F. Espenscheid, E. Willis, E. Matijević, and M. Kerker, J. Colloid. Sci. 20, 501 (1965).

W. F. Espenscheid, M. Kerker, and E. Matijević, J. Phys. Chem. 68, 3093 (1964).

M. Kerker, E. Matijević, W. F. Espenscheid, W. A. Farone, and S. Kitani, J. Colloid. Sci. 19, 213 (1964).

M. Kerker, E. Daby, G. L. Cohen, J. P. Kratohvil, and E. Matijević, J. Phys. Chem. 67, 2105 (1963).

M. Kerker and V. K. La Mer, J. Am. Chem. Soc. 72, 3516 (1950).

Kitani, S.

M. Kerker, E. Matijević, W. F. Espenscheid, W. A. Farone, and S. Kitani, J. Colloid. Sci. 19, 213 (1964).

Kratohvil, J. P.

M. Kerker, E. Daby, G. L. Cohen, J. P. Kratohvil, and E. Matijević, J. Phys. Chem. 67, 2105 (1963).

La Mer, V. K.

M. Kerker and V. K. La Mer, J. Am. Chem. Soc. 72, 3516 (1950).

D. Sinclair and V. K. La Mer, Chem. Revs. 44, 249 (1949).

I. Johnson and V. K. La Mer, J. Am. Chem. Soc. 69, 1184 (1947).

Lorenz, L.

L. Lorenz, Vidensk. Selsk. Skr. 6, (1890); Oeures Scientifique (Copenhagen, 1898), Vol. I, p. 405; A. E. H. Love, Proc. London Math. Soc. 30, 308 (1899); P. Debye, Ann. Physik 30, 57 (1909); J. W. Nicholson, Proc. London Math. Soc. 9, 67 (1910); 11, 277 (1912); T. S. Bromwich, Phil. Mag. 38, 144 (1919).

Matijevic, E.

W. F. Espenscheid, E. Willis, E. Matijević, and M. Kerker, J. Colloid. Sci. 20, 501 (1965).

M. Kerker, E. Matijević, W. F. Espenscheid, W. A. Farone, and S. Kitani, J. Colloid. Sci. 19, 213 (1964).

W. F. Espenscheid, M. Kerker, and E. Matijević, J. Phys. Chem. 68, 3093 (1964).

M. Kerker, E. Daby, G. L. Cohen, J. P. Kratohvil, and E. Matijević, J. Phys. Chem. 67, 2105 (1963).

McCarley, J. E.

J. E. McCarley, C. E. Green, and K. H. Horowitz, J. Opt. Soc. Am. 55, 355 (1965).

Mie, G.

G. Mie, Ann. Physik 25, 377 (1908).

Perrin, F. H.

A. C. Hardy and F. H. Perrin, The Principles of Optics (McGraw-Hill Book Co., New York, 1932).

Ray, B.

B. Ray, Proc. Indian Assoc. Cultiv. Sci. 7, 1 (1921).

Rayleigh, Lord

Lord Rayleigh, Phil. Mag. 41, 107, 274, 447 (1871); Scientific Papers (Dover Publications, Inc., New York, 1964) Vol., I, pp. 87–110.

Sinclair, D.

D. Sinclair and V. K. La Mer, Chem. Revs. 44, 249 (1949).

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Parlicles (John Wiley & Sons, New York, 1957).

Willis, E.

W. F. Espenscheid, E. Willis, E. Matijević, and M. Kerker, J. Colloid. Sci. 20, 501 (1965).

Other

Lord Rayleigh, Phil. Mag. 41, 107, 274, 447 (1871); Scientific Papers (Dover Publications, Inc., New York, 1964) Vol., I, pp. 87–110.

G. Mie, Ann. Physik 25, 377 (1908).

L. Lorenz, Vidensk. Selsk. Skr. 6, (1890); Oeures Scientifique (Copenhagen, 1898), Vol. I, p. 405; A. E. H. Love, Proc. London Math. Soc. 30, 308 (1899); P. Debye, Ann. Physik 30, 57 (1909); J. W. Nicholson, Proc. London Math. Soc. 9, 67 (1910); 11, 277 (1912); T. S. Bromwich, Phil. Mag. 38, 144 (1919).

M. Kerker, editor, Electromagnetic Scattering (Pergamon Press, New York, 1963).

R. H. Doremus, J. Chem. Phys. 40, 2389 (1964); 42, 414 (1965).

D. Sinclair and V. K. La Mer, Chem. Revs. 44, 249 (1949).

I. Johnson and V. K. La Mer, J. Am. Chem. Soc. 69, 1184 (1947).

M. Kerker, E. Daby, G. L. Cohen, J. P. Kratohvil, and E. Matijević, J. Phys. Chem. 67, 2105 (1963).

H. C. van de Hulst, Light Scattering by Small Parlicles (John Wiley & Sons, New York, 1957).

Committee on Colorimetry of the Optical Society of America, The Science of Color (Optical Society of America, Washington, D. C., 1963).

J. E. McCarley, C. E. Green, and K. H. Horowitz, J. Opt. Soc. Am. 55, 355 (1965).

R. T. Jacobsen, Ph.D. thesis, Clarkson College of Technology, Potsdam, New York, 1966.

Deposited as Document number 8954 with the ADI Auxiliary Publications Project, Photoduplication Service, Library of Congress, Washington 25, D. C. A copy may be secured by citing the Document number and by remitting $12.50 for photoprints, or $4.25 for 35 mm microfilm. Advance payment is required. Make checks or money orders payable to: Chief, Photoduplication Service, Library of Congress.

B. Ray, Proc. Indian Assoc. Cultiv. Sci. 7, 1 (1921).

M. Kerker, W. A. Farone, and W. F. Espenscheid, J. Colloid. Interface Sci. 21, 459 (1966).

W. F. Espenscheid, M. Kerker, and E. Matijević, J. Phys. Chem. 68, 3093 (1964).

M. Kerker and V. K. La Mer, J. Am. Chem. Soc. 72, 3516 (1950).

M. Kerker, E. Matijević, W. F. Espenscheid, W. A. Farone, and S. Kitani, J. Colloid. Sci. 19, 213 (1964).

W. F. Espenscheid, E. Willis, E. Matijević, and M. Kerker, J. Colloid. Sci. 20, 501 (1965).

A. C. Hardy and F. H. Perrin, The Principles of Optics (McGraw-Hill Book Co., New York, 1932).

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