Abstract

Monodisperse precipitates of silver bromide were made which had average grain sizes in the range of 0.1 to 1.0 μ. The optical transmittance of dilute turbid suspensions of the grains was measured over the wavelength range from 300 to 700 mμ. Suspensions in water and in gelatin coatings were measured and the results compared with the single, independent scattering theories of Rayleigh and of Mie. Satisfactory-agreement between theory and experiment was found in most cases, but some effects of multiple scattering were found in coatings where the centers of grains were separated by less than two grain diameters.

© 1962 Optical Society of America

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References

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  1. G. Mie, Ann. Physik 25, 377 (1908).
    [Crossref]
  2. A. N. Lowan, “Tables of scattering functions for spherical particles,” Natl. Bur. Standards A.S.M.-4, Washington, D.C. (1948).
  3. R. O. Gumprecht and C. M. Sliepcevich, “Tables of light scattering functions for spherical particles,” Engineering Research Institute, University of Michigan, Ann Arbor, Michigan, 1951.
  4. E. J. Meehan and W. H. Beattie, J. Phys. Chem. 64, 1006 (1960).
    [Crossref]
  5. E. J. Meehan and W. H. Beattie, J. Opt. Soc. Am. 49, 735 (1959).
    [Crossref]
  6. Y. Okamoto, Nachr. Akad. Wiss. Göttingen, Math.—physik. Kl. 14 (1956).
  7. D. C. Skillman, Kodak Research Laboratories (private communication).

1960 (1)

E. J. Meehan and W. H. Beattie, J. Phys. Chem. 64, 1006 (1960).
[Crossref]

1959 (1)

1956 (1)

Y. Okamoto, Nachr. Akad. Wiss. Göttingen, Math.—physik. Kl. 14 (1956).

1908 (1)

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

Beattie, W. H.

E. J. Meehan and W. H. Beattie, J. Phys. Chem. 64, 1006 (1960).
[Crossref]

E. J. Meehan and W. H. Beattie, J. Opt. Soc. Am. 49, 735 (1959).
[Crossref]

Gumprecht, R. O.

R. O. Gumprecht and C. M. Sliepcevich, “Tables of light scattering functions for spherical particles,” Engineering Research Institute, University of Michigan, Ann Arbor, Michigan, 1951.

Lowan, A. N.

A. N. Lowan, “Tables of scattering functions for spherical particles,” Natl. Bur. Standards A.S.M.-4, Washington, D.C. (1948).

Meehan, E. J.

E. J. Meehan and W. H. Beattie, J. Phys. Chem. 64, 1006 (1960).
[Crossref]

E. J. Meehan and W. H. Beattie, J. Opt. Soc. Am. 49, 735 (1959).
[Crossref]

Mie, G.

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

Okamoto, Y.

Y. Okamoto, Nachr. Akad. Wiss. Göttingen, Math.—physik. Kl. 14 (1956).

Skillman, D. C.

D. C. Skillman, Kodak Research Laboratories (private communication).

Sliepcevich, C. M.

R. O. Gumprecht and C. M. Sliepcevich, “Tables of light scattering functions for spherical particles,” Engineering Research Institute, University of Michigan, Ann Arbor, Michigan, 1951.

Ann. Physik (1)

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

J. Opt. Soc. Am. (1)

J. Phys. Chem. (1)

E. J. Meehan and W. H. Beattie, J. Phys. Chem. 64, 1006 (1960).
[Crossref]

Nachr. Akad. Wiss. Göttingen, Math.—physik. Kl. (1)

Y. Okamoto, Nachr. Akad. Wiss. Göttingen, Math.—physik. Kl. 14 (1956).

Other (3)

D. C. Skillman, Kodak Research Laboratories (private communication).

A. N. Lowan, “Tables of scattering functions for spherical particles,” Natl. Bur. Standards A.S.M.-4, Washington, D.C. (1948).

R. O. Gumprecht and C. M. Sliepcevich, “Tables of light scattering functions for spherical particles,” Engineering Research Institute, University of Michigan, Ann Arbor, Michigan, 1951.

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Figures (11)

Fig. 1
Fig. 1

Electron micrographs of some monodisperse silver halide precipitates. Top, AgCl cubes, 0.096-μ edge length; 2nd, AgBr spheres, 0.116-μ diameter; 3rd, AgBr cubes, 0.27-μ edge length; bottom, AgBr cubes, 0.81-μ edge length.

Fig. 2
Fig. 2

Observed Rayleigh scattering from fine-grain AgBr suspension in water.

Fig. 3
Fig. 3

Mie scattering from AgBr in water. Cell length, 1 cm. concentration of AgBr is 1.38 × 10−4 g/ml. Grain sizes range from 0.27 to 1.3 μ.

Fig. 4
Fig. 4

Measured dependence of turbidity in water on grain size at three separate wavelengths.

Fig. 5
Fig. 5

Computations from the Mie theory of the relation of the crystal diameter and the wavelength of maximum or minimum turbidity for AgBr in water.

Fig. 6
Fig. 6

Comparison of average grain size from electron micrographs and from the wavelength of maximum or minimum turbidity in water.

Fig. 7
Fig. 7

Comparison of average grain size from electron micrographs and from the magnitude of the turbidity in water at the primary maximum.

Fig. 8
Fig. 8

Optical density caused by absorption in an average thickness of 0.21 μ of AgBr. Curve A, wavelength-dependence in a uniform sheet; Curve B, grain-size dependence at the wavelength 300 mμ.

Fig. 9
Fig. 9

Turbidity of AgBr grains of different sizes coated in gelatin. Average thickness of AgBr is 0.15 μ and of gelatin 1.4 μ.

Fig. 10
Fig. 10

Turbidity of single-layer coatings of AgBr in gelatin. Cubes of 0.49-μ edge length. Separation of centers: A, 1.59μ; B, 1.18 μ; C, 0.61 μ.

Fig. 11
Fig. 11

Universal turbidity curves for AgBr. Computed and observed curves for suspensions in water and in gelatin coatings.

Tables (6)

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Table I Crystal-size determination from the magnitude of the turbidity.

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Table II Ratio of observed to computed optical density of suspensions in water.

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Table III Effect on optical density of a tenfold change in silver bromide concentration from 1.38 × 10−4 to 1.38 × 10−3 g/ml.

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Table IV Test of Beer’s law, using a concentration of 1.38 × 10−3 in 1-mm cell and a concentration of 1.38 × 10−4 in 1-cm cell.

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Table V Comparison of observed and calculated turbidity for suspensions coated in gelatin.

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Table VI Measured values of turbidity with changing AgBr and gelatin thickness.

Equations (1)

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K = 8 3 ( π d μ 0 λ ) 4 ( m 2 1 m 2 + 2 ) 2 .