Abstract

The tristimulus color system is used to describe the colors of the light scattered by spheres with radii a = 0.2, 0.3, 0.4, 0.5, 0.6, 0.8, 1.0, and 1.2 μ for real refractive indices m = 1.31 and 1.46 and by spheres with radii a = 0.1, 0.2, 0.4μ 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.

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 a>0.8 μ, the scattered light is uniformly yellow. At intermediate sizes 0.2 μa≤0.8 μ 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.

© 1966 Optical Society of America

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References

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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).
    [Crossref]
  3. L. Lorenz, Vidensk. Selsk. Skr. 6, (1890);Oeuvres 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);Proc. London Math. Soc. 11, 277 (1912);T. S. Bromwich, Phil. Mag. 38, 144 (1919).
    [Crossref]
  4. M. Kerker, editor, Electromagnetic Scattering (Pergamon Press, New York, 1963).
  5. R. H. Doremus, J. Chem. Phys. 40, 2389 (1964);J. Chem. Phys. 42, 414 (1965).
    [Crossref]
  6. D. Sinclair and V. K. La Mer, Chem. Revs. 44, 249 (1949).
    [Crossref]
  7. I. Johnson and V. K. La Mer, J. Am. Chem. Soc. 69, 1184 (1947).
    [Crossref] [PubMed]
  8. M. Kerker, E. Daby, G. L. Cohen, J. P. Kratohvil, and E. Matijević, J. Phys. Chem. 67, 2105 (1963).
    [Crossref]
  9. H. C. van de Hulst, Light Scattering by Small Particles (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).
    [Crossref]
  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).
    [Crossref]
  16. W. F. Espenscheid, M. Kerker, and E. Matijević, J. Phys. Chem. 68, 3093 (1964).
    [Crossref]
  17. M. Kerker and V. K. La Mer, J. Am. Chem. Soc. 72, 3516 (1950).
    [Crossref]
  18. M. Kerker, E. Matijević, W. F. Espenscheid, W. A. Farone, and S. Kitani, J. Colloid. Sci. 19, 213 (1964).
    [Crossref]
  19. W. F. Espenscheid, E. Willis, E. Matijević, and M. Kerker, J. Colloid. Sci. 20, 501 (1965).
    [Crossref] [PubMed]
  20. A. C. Hardy and F. H. Perrin, The Principles of Optics (McGraw-Hill Book Co., New York, 1932).

1966 (1)

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

1965 (2)

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

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

1964 (3)

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

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

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

1963 (1)

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

1950 (1)

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

1949 (1)

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

1947 (1)

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

1921 (1)

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

1908 (1)

G. Mie, Ann. Physik 25, 377 (1908).
[Crossref]

1890 (1)

L. Lorenz, Vidensk. Selsk. Skr. 6, (1890);Oeuvres 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);Proc. London Math. Soc. 11, 277 (1912);T. S. Bromwich, Phil. Mag. 38, 144 (1919).
[Crossref]

1871 (1)

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).
[Crossref]

Daby, E.

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

Doremus, R. H.

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

Espenscheid, W. F.

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

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

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

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

Farone, W. A.

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

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

Green, C. E.

Hardy, A. C.

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

Horowitz, K. H.

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).
[Crossref] [PubMed]

Kerker, M.

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

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

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

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

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

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

Kitani, S.

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

Kratohvil, J. P.

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

La Mer, V. K.

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

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

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

Lorenz, L.

L. Lorenz, Vidensk. Selsk. Skr. 6, (1890);Oeuvres 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);Proc. London Math. Soc. 11, 277 (1912);T. S. Bromwich, Phil. Mag. 38, 144 (1919).
[Crossref]

Matijevic, E.

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

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

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

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

McCarley, J. E.

Mie, G.

G. Mie, Ann. Physik 25, 377 (1908).
[Crossref]

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).
[Crossref]

van de Hulst, H. C.

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

Willis, E.

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

Ann. Physik (1)

G. Mie, Ann. Physik 25, 377 (1908).
[Crossref]

Chem. Revs. (1)

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

J. Am. Chem. Soc. (2)

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

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

J. Chem. Phys. (1)

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

J. Colloid. Interface Sci. (1)

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

J. Colloid. Sci. (2)

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

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

J. Opt. Soc. Am. (1)

J. Phys. Chem. (2)

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

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

Phil. Mag. (1)

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

Proc. Indian Assoc. Cultiv. Sci. (1)

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

Vidensk. Selsk. Skr. (1)

L. Lorenz, Vidensk. Selsk. Skr. 6, (1890);Oeuvres 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);Proc. London Math. Soc. 11, 277 (1912);T. S. Bromwich, Phil. Mag. 38, 144 (1919).
[Crossref]

Other (6)

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

H. C. van de Hulst, Light Scattering by Small Particles (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).

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.

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

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Figures (6)

F. 1
F. 1

Relative luminous intensity of the perpendicular component of the scattered light as a function of angles of observation for m = 1.46, a = 0.4, 0.8, 1.2 μ, and 3200°K source.

F. 2
F. 2

Relative luminous intensity of the parallel component of the scattered light as a function of the angle of observation for m = 1.46, a = 0.4, 0.8, 1.2 μ, and 3200°K source.

F. 3
F. 3

Relative luminous intensity of the perpendicular and the parallel components of the scattered light as a function of angle of observation for vanadium pentoxide, a = 0.4 μ, and 3200°K source. The parallel component is displaced upwards by one order of magnitude.

F. 4
F. 4

Relative luminous intensity and color of the forward scattered light (θ = 0) as a function of particle radius for m = 1.31 and 1.46 and 3200°K source.

F. 5
F. 5

Relative luminous intensity and color of the back scattered light (θ = 180°) as a function of particle radius for m = 1.31 and 1.46 and 3200°K source.

F. 6
F. 6

Variation of the polarization of the scattered light as a function of radius for θ = 150°, 160°, and 170°, m = 1.46, and 3200°K source.

Tables (7)

Tables Icon

Table I Refractive index of vanadium pentoxide.

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Table II Notation for dominant wavelengths.

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Table III Colors of the vertical component of the scattered light.

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Table IV Colors of the vertical component of the scattered light.

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Table V Angular location of red and green orders.

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Table VI Angular location of red and green orders.

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Table VII Colors of the vertical component of the scattered light V2O5 spheres; 3200°K source.

Equations (7)

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

I 1 ( θ ) = λ 0 λ 2 P λ 4 π 2 r 2 i 1 f ( a ) dad λ ,
X 1 = k λ 0 λ 2 P λ x ¯ λ i 1 f ( a ) dad λ
Y 1 = k λ 0 λ 2 P λ y ¯ λ i 1 f ( a ) dad λ
Z 1 = k λ 0 λ 2 P λ z ¯ λ i 1 f ( a ) dad λ .
x 1 = X 1 / ( X 1 + Y 1 + Z 1 )
y 1 = Y 1 / ( X 1 + Y 1 + Z 1 )
P = ( I 1 I 2 ) / ( I 1 + I 2 ) .