Abstract

The refractive index of submillimeter glass beads has been measured by means of a novel, to our knowledge, procedure with reference liquids that does not require close index matching and therefore avoids the use of toxic compounds for high-index glasses (i.e., n ≥ 1.8). The method is based on the analysis of the light refracted by a monolayer of beads in comparison with ray-tracing simulations. For the three different types of glass beads investigated a satisfactory fit is achieved by the assumption of a radial variation of the refractive index inside the beads. This is ascribed to the tensile and compressive stresses originating inside the beads during rapid solidification of the glass.

© 1997 Optical Society of America

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References

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  1. H. Lein, R. S. Tankin, “Natural convection in porous media–I. Nonfreezing,” Int. J. Heat Mass Transfer 35, 175–186 (1992).
    [Crossref]
  2. N. H. Hartshorne, A. Stuart, Crystals and the Polarizing Microscope (Arnold, London, 1970), p. 561.
  3. R. P. Cargille Laboratories, Inc., “Optical liquids precaution sheet,” (Cedar Grove, N.J., 1995).
  4. See, for example, Society of Automotive Engineers information report J784a (SAE, Warrendale, Pa., 1971), pp. 3–11.
  5. For a comprehensive review with recent developments and applications of the Christiansen effect see, for example, K. Balasubramanian, M. R. Jacobson, H. A. Macleod, “New Christiansen filters,” Appl. Opt. 31, 1574–1587 (1992).

1992 (2)

Balasubramanian, K.

Hartshorne, N. H.

N. H. Hartshorne, A. Stuart, Crystals and the Polarizing Microscope (Arnold, London, 1970), p. 561.

Jacobson, M. R.

Lein, H.

H. Lein, R. S. Tankin, “Natural convection in porous media–I. Nonfreezing,” Int. J. Heat Mass Transfer 35, 175–186 (1992).
[Crossref]

Macleod, H. A.

Stuart, A.

N. H. Hartshorne, A. Stuart, Crystals and the Polarizing Microscope (Arnold, London, 1970), p. 561.

Tankin, R. S.

H. Lein, R. S. Tankin, “Natural convection in porous media–I. Nonfreezing,” Int. J. Heat Mass Transfer 35, 175–186 (1992).
[Crossref]

Appl. Opt. (1)

Int. J. Heat Mass Transfer (1)

H. Lein, R. S. Tankin, “Natural convection in porous media–I. Nonfreezing,” Int. J. Heat Mass Transfer 35, 175–186 (1992).
[Crossref]

Other (3)

N. H. Hartshorne, A. Stuart, Crystals and the Polarizing Microscope (Arnold, London, 1970), p. 561.

R. P. Cargille Laboratories, Inc., “Optical liquids precaution sheet,” (Cedar Grove, N.J., 1995).

See, for example, Society of Automotive Engineers information report J784a (SAE, Warrendale, Pa., 1971), pp. 3–11.

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Figures (12)

Fig. 1
Fig. 1

Schematic diagram of the experimental setup with the cell–screen optical path in the enlarged area.

Fig. 2
Fig. 2

Intensity distribution on the screen of the light refracted by a monolayer of test beads with a nominal refractive index of ns = 1.65 in an optical liquid with a refractive index of nl = 1.600. The dots represent the experimental data. The solid curves show the results of the numerical simulations with the planar approach for different values of the parameter ns.

Fig. 3
Fig. 3

Same as for Fig. 2 for test beads with ns = 1.65 and nl = 1.500.

Fig. 4
Fig. 4

Same as for Fig. 2 for test beads with ns = 1.515 and nl = 1.460.

Fig. 5
Fig. 5

Same as for Fig. 2 for test beads with ns = 1.515 and nl = 1.360.

Fig. 6
Fig. 6

Same as for Fig. 2 for the high-index unknown beads in an optical liquid with nl = 1.700.

Fig. 7
Fig. 7

Three-dimensional plot of the light intensity distribution obtained with the 3-D numerical simulation for the case of a single glass sphere with ns = 1.65 in an optical liquid with nl = 1.500.

Fig. 8
Fig. 8

Comparison between the simulation for the 3-D model (discrete points) and that for the planar approach (solid lines) for beads with (a) ns = 1.65 and (b) ns = 1.515 in liquids with values of nl as displayed.

Fig. 9
Fig. 9

Simulation of the light ray path through a single glass bead. The refractive index is assumed to be (a) uniform inside the bead with a value ns = 3 or (b) linearly dependent on the distance from the center with an average value of = 3 and a range of variation of Δn = 0.45. In both cases the host-liquid refractive index is nl = 1.700.

Fig. 10
Fig. 10

Light intensity distribution for test beads with ns = 1.65 in an optical liquid with nl = 1.500. The dots represent the experimental data. The curves show the results of the numerical simulations by the assumption that the refractive index varies linearly over the range of variation of Δn = 0.04 around the average values = 1.67 (solid curve) or = 1.65 (dashed curve).

Fig. 11
Fig. 11

Same as for Fig. 10 but by the assumption of an average value of = 1.66 and ranges of variation of Δn = 0.06 (solid curve), Δn = 0.04 (dashed curve), and Δn = 0.02 (dashed–dotted curve).

Fig. 12
Fig. 12

Light intensity distribution for the high-index beads in an optical liquid with nl = 1.700 by assumption of an average value of = 1.90 and values of the range of variation of Δn = 0.04 and Δn = 0.02, as displayed in the curve labels.

Equations (3)

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Ixdx=Ixdx;
Ix=Ixxxx,
nr=n¯+Δn2rR-1,

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