Abstract

This is an experimental study of multiple scattering by a polystyrene latex whose particles have a modal diameter of 1.277 μ. A special rectangular cell was constructed to correspond to an infinite plane-parallel slab. The experiments were carried out for two wavelengths, λ0=0.546 and 0.436 μ, for two cell thicknesses 0.089 and 0.183 cm, and for seven concentrations, ranging from 1.051×10−5 to 1.058×10−2 g/g. The angular range was from 0° to 90°. The higher angles were made accessible by placing the scattering cell in a cylindrical jacket containing Nujol. Extensive theoretical calculations were carried out with the aid of the Hartel theory for each of the above cases. The agreement between the experimental and theoretical results was excellent.

© 1965 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. W. Trinks, Ann. Physik 22, 561 (1935).
    [Crossref]
  2. O. Lillesaeter, Proceedings of the Eleventh Weather Radar Conference, pp. 192–193 (1964), Am. Meteorol. Soc., Boston, Massachusetts.
  3. S. W. Churchill, G. C. Clark, and C. M. Sliepcevich, Discussions Faraday Soc. 30, 192 (1960).
    [Crossref]
  4. L. Chi-chen, Sci. Sinica Peking 12, 695 (1963).
  5. P. Debye in Electromagnetic Scattering, M. Kerker, ed. (Pergamon Press, London, 1963).
  6. M. Kerker, ed., Electromagnetic Scattering (Pergamon Press, London, 1963). See papers by D. Stigter, J. Th. G. Overbeek, A. Vrij, H. F. Huisman, and S. N. Timasheff.
  7. Ref. 6. See papers in Part 6, “Multiple Scattering.”
  8. D. H. Woodward, “Multiple Light Scattering by Spherical Dielectric Particles,” Ph.D. thesis, University of Colorado (1963).
  9. D. H. Woodward, Appl. Opt. 2, 1205 (1963).
    [Crossref]
  10. D. H. Woodward, J. Opt. Soc. Am. 54, 1325 (1964).
    [Crossref]
  11. G. Dezelić and J. P. Kratohvil, J. Colloid Sci. 16, 561 (1961).
    [Crossref]
  12. S. H. Maron, P. E. Pierce, and I. N. Ulevitch, J. Colloid Sci. 18, 470 (1963).
    [Crossref]
  13. W. Heller and M. Wallach, J. Phys. Chem. 68, 931 (1964).
    [Crossref]
  14. M. Kerker and E. Matijević, J. Opt. Soc. Am. 50, 722 (1960).
    [Crossref]
  15. W. Hartel, Licht 10, 141 (1940).
  16. J. P. Kratohvil, J. Colloid Sci. (to be published).
  17. H. C. van de Hulst, Light Scattering by Small Particles (John Wiley & Sons, Inc., New York, 1957), p. 126.
  18. G. C. Clark, C. M. Chu, and S. W. Churchill, J. Opt. Soc. Am. 47, 81 (1957).
    [Crossref]
  19. W. F. Espenschied, M. Kerker, and E. Matijević, J. Phys. Chem. 68, 3093 (1964).
    [Crossref]
  20. J. P. Kratohvil and C. Smart, J. Colloid Sci (to be published).
  21. M. Kerker, E. Matijević, W. F. Espenscheid, W. A. Farone, and S. Kitani, J. Colloid Sci. 19, 213 (1964).
    [Crossref]
  22. W. J. Pangonis, W. Heller, and A. Jacobson, Tables of Light Scattering Functions for Spherical Particles (Wayne State University Press, Michigan, 1957).

1964 (4)

D. H. Woodward, J. Opt. Soc. Am. 54, 1325 (1964).
[Crossref]

W. Heller and M. Wallach, J. Phys. Chem. 68, 931 (1964).
[Crossref]

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

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

1963 (3)

S. H. Maron, P. E. Pierce, and I. N. Ulevitch, J. Colloid Sci. 18, 470 (1963).
[Crossref]

L. Chi-chen, Sci. Sinica Peking 12, 695 (1963).

D. H. Woodward, Appl. Opt. 2, 1205 (1963).
[Crossref]

1961 (1)

G. Dezelić and J. P. Kratohvil, J. Colloid Sci. 16, 561 (1961).
[Crossref]

1960 (2)

M. Kerker and E. Matijević, J. Opt. Soc. Am. 50, 722 (1960).
[Crossref]

S. W. Churchill, G. C. Clark, and C. M. Sliepcevich, Discussions Faraday Soc. 30, 192 (1960).
[Crossref]

1957 (1)

1940 (1)

W. Hartel, Licht 10, 141 (1940).

1935 (1)

W. Trinks, Ann. Physik 22, 561 (1935).
[Crossref]

Chi-chen, L.

L. Chi-chen, Sci. Sinica Peking 12, 695 (1963).

Chu, C. M.

Churchill, S. W.

S. W. Churchill, G. C. Clark, and C. M. Sliepcevich, Discussions Faraday Soc. 30, 192 (1960).
[Crossref]

G. C. Clark, C. M. Chu, and S. W. Churchill, J. Opt. Soc. Am. 47, 81 (1957).
[Crossref]

Clark, G. C.

S. W. Churchill, G. C. Clark, and C. M. Sliepcevich, Discussions Faraday Soc. 30, 192 (1960).
[Crossref]

G. C. Clark, C. M. Chu, and S. W. Churchill, J. Opt. Soc. Am. 47, 81 (1957).
[Crossref]

Debye, P.

P. Debye in Electromagnetic Scattering, M. Kerker, ed. (Pergamon Press, London, 1963).

Dezelic, G.

G. Dezelić and J. P. Kratohvil, J. Colloid Sci. 16, 561 (1961).
[Crossref]

Espenscheid, W. F.

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

Espenschied, W. F.

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

Farone, W. A.

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

Hartel, W.

W. Hartel, Licht 10, 141 (1940).

Heller, W.

W. Heller and M. Wallach, J. Phys. Chem. 68, 931 (1964).
[Crossref]

W. J. Pangonis, W. Heller, and A. Jacobson, Tables of Light Scattering Functions for Spherical Particles (Wayne State University Press, Michigan, 1957).

Huisman, H. F.

M. Kerker, ed., Electromagnetic Scattering (Pergamon Press, London, 1963). See papers by D. Stigter, J. Th. G. Overbeek, A. Vrij, H. F. Huisman, and S. N. Timasheff.

Jacobson, A.

W. J. Pangonis, W. Heller, and A. Jacobson, Tables of Light Scattering Functions for Spherical Particles (Wayne State University Press, Michigan, 1957).

Kerker, M.

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

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

M. Kerker and E. Matijević, J. Opt. Soc. Am. 50, 722 (1960).
[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.

G. Dezelić and J. P. Kratohvil, J. Colloid Sci. 16, 561 (1961).
[Crossref]

J. P. Kratohvil, J. Colloid Sci. (to be published).

J. P. Kratohvil and C. Smart, J. Colloid Sci (to be published).

Lillesaeter, O.

O. Lillesaeter, Proceedings of the Eleventh Weather Radar Conference, pp. 192–193 (1964), Am. Meteorol. Soc., Boston, Massachusetts.

Maron, S. H.

S. H. Maron, P. E. Pierce, and I. N. Ulevitch, J. Colloid Sci. 18, 470 (1963).
[Crossref]

Matijevic, E.

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

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

M. Kerker and E. Matijević, J. Opt. Soc. Am. 50, 722 (1960).
[Crossref]

Overbeek, J. Th. G.

M. Kerker, ed., Electromagnetic Scattering (Pergamon Press, London, 1963). See papers by D. Stigter, J. Th. G. Overbeek, A. Vrij, H. F. Huisman, and S. N. Timasheff.

Pangonis, W. J.

W. J. Pangonis, W. Heller, and A. Jacobson, Tables of Light Scattering Functions for Spherical Particles (Wayne State University Press, Michigan, 1957).

Pierce, P. E.

S. H. Maron, P. E. Pierce, and I. N. Ulevitch, J. Colloid Sci. 18, 470 (1963).
[Crossref]

Sliepcevich, C. M.

S. W. Churchill, G. C. Clark, and C. M. Sliepcevich, Discussions Faraday Soc. 30, 192 (1960).
[Crossref]

Smart, C.

J. P. Kratohvil and C. Smart, J. Colloid Sci (to be published).

Stigter, D.

M. Kerker, ed., Electromagnetic Scattering (Pergamon Press, London, 1963). See papers by D. Stigter, J. Th. G. Overbeek, A. Vrij, H. F. Huisman, and S. N. Timasheff.

Timasheff, S. N.

M. Kerker, ed., Electromagnetic Scattering (Pergamon Press, London, 1963). See papers by D. Stigter, J. Th. G. Overbeek, A. Vrij, H. F. Huisman, and S. N. Timasheff.

Trinks, W.

W. Trinks, Ann. Physik 22, 561 (1935).
[Crossref]

Ulevitch, I. N.

S. H. Maron, P. E. Pierce, and I. N. Ulevitch, J. Colloid Sci. 18, 470 (1963).
[Crossref]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (John Wiley & Sons, Inc., New York, 1957), p. 126.

Vrij, A.

M. Kerker, ed., Electromagnetic Scattering (Pergamon Press, London, 1963). See papers by D. Stigter, J. Th. G. Overbeek, A. Vrij, H. F. Huisman, and S. N. Timasheff.

Wallach, M.

W. Heller and M. Wallach, J. Phys. Chem. 68, 931 (1964).
[Crossref]

Woodward, D. H.

D. H. Woodward, J. Opt. Soc. Am. 54, 1325 (1964).
[Crossref]

D. H. Woodward, Appl. Opt. 2, 1205 (1963).
[Crossref]

D. H. Woodward, “Multiple Light Scattering by Spherical Dielectric Particles,” Ph.D. thesis, University of Colorado (1963).

Ann. Physik (1)

W. Trinks, Ann. Physik 22, 561 (1935).
[Crossref]

Appl. Opt. (1)

Discussions Faraday Soc. (1)

S. W. Churchill, G. C. Clark, and C. M. Sliepcevich, Discussions Faraday Soc. 30, 192 (1960).
[Crossref]

J. Colloid Sci. (3)

G. Dezelić and J. P. Kratohvil, J. Colloid Sci. 16, 561 (1961).
[Crossref]

S. H. Maron, P. E. Pierce, and I. N. Ulevitch, J. Colloid Sci. 18, 470 (1963).
[Crossref]

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

J. Opt. Soc. Am. (3)

J. Phys. Chem. (2)

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

W. Heller and M. Wallach, J. Phys. Chem. 68, 931 (1964).
[Crossref]

Licht (1)

W. Hartel, Licht 10, 141 (1940).

Sci. Sinica Peking (1)

L. Chi-chen, Sci. Sinica Peking 12, 695 (1963).

Other (9)

P. Debye in Electromagnetic Scattering, M. Kerker, ed. (Pergamon Press, London, 1963).

M. Kerker, ed., Electromagnetic Scattering (Pergamon Press, London, 1963). See papers by D. Stigter, J. Th. G. Overbeek, A. Vrij, H. F. Huisman, and S. N. Timasheff.

Ref. 6. See papers in Part 6, “Multiple Scattering.”

D. H. Woodward, “Multiple Light Scattering by Spherical Dielectric Particles,” Ph.D. thesis, University of Colorado (1963).

O. Lillesaeter, Proceedings of the Eleventh Weather Radar Conference, pp. 192–193 (1964), Am. Meteorol. Soc., Boston, Massachusetts.

J. P. Kratohvil, J. Colloid Sci. (to be published).

H. C. van de Hulst, Light Scattering by Small Particles (John Wiley & Sons, Inc., New York, 1957), p. 126.

J. P. Kratohvil and C. Smart, J. Colloid Sci (to be published).

W. J. Pangonis, W. Heller, and A. Jacobson, Tables of Light Scattering Functions for Spherical Particles (Wayne State University Press, Michigan, 1957).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

F. 1
F. 1

Optical system for multiple scattering experiments. A, Hg arc; B, monochromatic filler; C, lens; D, light stops; E, light stops; F, cell; G, cylindrical jacket filled with Nujol; H, light stops; I, analyzer; J, photomultiplier.

F. 2
F. 2

Rayleigh ratio vs angle of observation for path length x=0.183 cm and wavelength λ0=436 mμ. Concentrations are 1.051×10−5 g/g (circles), 1.074×10−4 (squares), and 3.237×10−4 (triangles).

F. 3
F. 3

Rayleigh ratio vs angle of observation for path length x=0.183 cm and wavelength λ0=436 mμ. Concentrations are 9.928×10−4 g/g (circles), 3.058×10−3 (squares), and 1.058×10−2 (triangles).

F. 4
F. 4

Rayleigh ratio vs angle of observation for path length x=0.089 cm and wavelength λ0=436 mμ. Concentrations are 1.051×10−5 g/g (circles), 1.074×10−4 (squares), and 3.237×10−4 (triangles).

F. 5
F. 5

Rayleigh ratio vs angle of observation for path length x=0.089 cm and wavelength λ0=436 mμ. Concentrations are 9.928×10−4 g/g (circles), 3.058×10−3 (squares), and 1.058×10−2 (triangles).

F. 6
F. 6

Rayleigh ratio vs angle of observation for path length x=0.183 cm and wavelength λ0=546 mμ. Concentrations are 1.051×10−5 g/g (circles), 1.074×10−4 (squares), and 3.237×10−4 (triangles).

F. 7
F. 7

Rayleigh ratio vs angle of observation for path length x=0.183 cm and wavelength λ0=546 mμ. Concentrations are 9.928×10−4 g/g (circles), 3.058×10−3 (squares), and 1.058×10−2 (triangles).

F. 8
F. 8

Rayleigh ratio vs angle of observation for path length x=0.089 cm and wavelength λ0=546 mμ. Concentrations are 1.051×10−5 g/g (circles), 1.074×10−4 (squares), and 3.237×10−4 (triangles).

F. 9
F. 9

Rayleigh ratio vs angle of observation for path length x=0.089 cm and wavelength λ0=546 mμ. Concentrations are 9.928×10−4 g/g (circles), 3.058×10−3 (squares), and 1.058×10−2 (triangles).

Tables (2)

Tables Icon

Table I Optical depths D of the seven latexes studied.

Tables Icon

Table II Values of the index k for the maximum value of the intensity function Qmax as well as the low and high values, QL and QH.

Equations (22)

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

Δ I = { 1 2 ( a / A ) 3 q + ( a / A ) 6 [ p ] 2 } 1 1 .
p = ( m 2 1 ) / ( m 2 + 2 ) = q i q ,
I ( θ ) = n = 0 A n P n ( cos θ ) ,
I ( θ ) = [ k = 1 ( NFx ) k k ! e NFx ] × [ n = 0 1 4 π ( 2 n + 1 ) ( A n A 0 ( 2 n + 1 ) ) k P n ( cos θ ) ] ,
Ω f k ( θ ) d Ω = 1 ,
k = 0 Q k ( x ) = 1 .
I k ( θ ) = Q k ( x ) f k ( θ ) ,
I ( θ ) = k = 1 Q k f k ( θ ) .
F ¯ = 0 p ( α ) F d α ,
Q ¯ k = ( N F ¯ x ) k k ! e N F ¯ x .
I 1 ( θ ) = 0 I ( θ , α ) p ( α ) d α = 0 n = 0 A n P n ( cos θ ) p ( α ) d α .
f 1 ( θ ) = 0 n = 0 A n P n ( cos θ ) p ( α ) d α 4 π 0 A 0 p ( α ) d α ,
f 1 ( θ ) = 1 4 π n = 0 ( 0 A n p ( α ) d α 0 A 0 p ( α ) d α ) P n ( cos θ )
= 1 4 π n = 0 ā n P n ( cos θ ) ,
NFx = 3 π Q SCA c / 2 ρ α λ ,
R θ = [ I ( θ ) ] / x ,
sin θ = sin θ E / n w ,
sin θ = ( sin θ E ) n p / n w ,
V ( θ ) sin θ = const = V 90 .
V ( θ ) cos θ = const = V 0 .
R θ = n 2 T D π h ( 1.049 ) R W R c a r r 1 ( 1 f ) 3 ( G θ G W )
D = τ x .