Abstract

High-order rainbows, formed by a pendant drop, with an order number as high as 32 have been observed, to our knowledge, for the first time. We measured the refractive index of distilled-water drops, with an accuracy of ∼2 parts in 104, by exploiting some of the high-order rainbows.

© 1996 Optical Society of America

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References

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  1. K. Sassen, “Angular scattering and rainbow formation in pendant drops,” J. Opt. Soc. Am. 69, 1083–1089 (1979).
    [CrossRef]
  2. J. Walker, “Multiple rainbows from single drops of water and other liquids,” Am. J. Phys. 44, 424–433 (1976); J. Walker, “How to create and observe a dozen rainbows in a single drop of water,” Sci. Am. 237, 138–144 (July1977).
    [CrossRef]
  3. J. A. Lock, “Theory of the observations made of high-order rainbows from a single water droplet,” Appl. Opt. 26, 5291–5298 (1987).
    [CrossRef] [PubMed]
  4. R. T. Wang and H. C. van de Hulst, “Rainbows: Mie computations and the Airy approximation,” Appl. Opt. 30, 106–117 (1991).
    [CrossRef] [PubMed]
  5. S. D. Mobbs, “Theory of the rainbow,” J. Opt. Soc. Am. 69, 1089–1092 (1979) and references therein.
    [CrossRef]
  6. W. Mahmood bin Mat Yunus and A. bin Abdul Rahman, “Refractive index of solutions at high concentrations,” Appl. Opt. 27, 3341–3343 (1988).
    [CrossRef]
  7. K. Kuhler, E. L. Dereniak, and M. Buchanan, “Measurement of the index of refraction of the plastic phenoxy PKFE,” Appl. Opt. 30, 1711–1714 (1991).
    [CrossRef] [PubMed]
  8. E. Moreels, C. de Greef, and R. Finsy, “Laser light refractometer,” Appl. Opt. 23, 3010–3013 (1984).
    [CrossRef] [PubMed]
  9. S. Sainov and N. Dushkina, “Simple laser microrefractometer,” Appl. Opt. 29, 1406–1410 (1990).
    [CrossRef]
  10. M. V. R. K. Murty and R. P. Shukla, “Simple method for measuring the refractive index of a liquid or glass wedge,” Opt. Eng. 22, 227–230 (1983).
    [CrossRef]
  11. S. Nemoto, “Measurement of the refractive index of liquid using laser beam displacement,” Appl. Opt. 31, 6690–6694 (1992).
    [CrossRef] [PubMed]
  12. P. Chylek, V. Ramaswamy, A. Ashkin, and J. M. Dziedzic, “Simultaneous determination of refractive index and size of spherical dielectric particles from light scattering data,” Appl. Opt. 22, 2302–2307 (1983).
    [CrossRef] [PubMed]
  13. Cooling that was due to evaporation was estimated to be less than 1 °C, which implies an increase of less than 0.0001 in the refractive index.
  14. H. Eisenberg, “Equation for refractive index of water,” J. Chem. Phys. 43, 3887–3892 (1965).
    [CrossRef]

1992 (1)

1991 (2)

1990 (1)

1988 (1)

1987 (1)

1984 (1)

1983 (2)

1979 (2)

1976 (1)

J. Walker, “Multiple rainbows from single drops of water and other liquids,” Am. J. Phys. 44, 424–433 (1976); J. Walker, “How to create and observe a dozen rainbows in a single drop of water,” Sci. Am. 237, 138–144 (July1977).
[CrossRef]

1965 (1)

H. Eisenberg, “Equation for refractive index of water,” J. Chem. Phys. 43, 3887–3892 (1965).
[CrossRef]

Ashkin, A.

bin Abdul Rahman, A.

Buchanan, M.

Chylek, P.

de Greef, C.

Dereniak, E. L.

Dushkina, N.

Dziedzic, J. M.

Eisenberg, H.

H. Eisenberg, “Equation for refractive index of water,” J. Chem. Phys. 43, 3887–3892 (1965).
[CrossRef]

Finsy, R.

Kuhler, K.

Lock, J. A.

Mahmood bin Mat Yunus, W.

Mobbs, S. D.

Moreels, E.

Murty, M. V. R. K.

M. V. R. K. Murty and R. P. Shukla, “Simple method for measuring the refractive index of a liquid or glass wedge,” Opt. Eng. 22, 227–230 (1983).
[CrossRef]

Nemoto, S.

Ramaswamy, V.

Sainov, S.

Sassen, K.

Shukla, R. P.

M. V. R. K. Murty and R. P. Shukla, “Simple method for measuring the refractive index of a liquid or glass wedge,” Opt. Eng. 22, 227–230 (1983).
[CrossRef]

van de Hulst, H. C.

Walker, J.

J. Walker, “Multiple rainbows from single drops of water and other liquids,” Am. J. Phys. 44, 424–433 (1976); J. Walker, “How to create and observe a dozen rainbows in a single drop of water,” Sci. Am. 237, 138–144 (July1977).
[CrossRef]

Wang, R. T.

Am. J. Phys. (1)

J. Walker, “Multiple rainbows from single drops of water and other liquids,” Am. J. Phys. 44, 424–433 (1976); J. Walker, “How to create and observe a dozen rainbows in a single drop of water,” Sci. Am. 237, 138–144 (July1977).
[CrossRef]

Appl. Opt. (8)

J. Chem. Phys. (1)

H. Eisenberg, “Equation for refractive index of water,” J. Chem. Phys. 43, 3887–3892 (1965).
[CrossRef]

J. Opt. Soc. Am. (2)

Opt. Eng. (1)

M. V. R. K. Murty and R. P. Shukla, “Simple method for measuring the refractive index of a liquid or glass wedge,” Opt. Eng. 22, 227–230 (1983).
[CrossRef]

Other (1)

Cooling that was due to evaporation was estimated to be less than 1 °C, which implies an increase of less than 0.0001 in the refractive index.

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Figures (3)

Fig. 1
Fig. 1

Schematic diagram of the experimental setup. The circle represents the droplet in the equatorial plane, and the laser beam is propagating along the positive x direction.

Fig. 2
Fig. 2

Intensity patterns of (a) sixth-order, (b) ninth-order, (c) eleventh-order rainbows and their supernumerary arcs. The scale below each pattern shows the scale of angle position. One division is 1°.

Fig. 3
Fig. 3

Angular intensity distribution of the nineteenth-order rainbow superimposed on the supernumerary arcs of the sixth-order rainbow. The long and the short arrows indicate the principal maximum and the first minimum of the nineteenth-order rainbow, respectively.

Tables (1)

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Table 1 Measured and Theoretical Values of θmax(p, n) and θmin(p, n)a

Equations (3)

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θ tot = 2 π l + θ 0 ( p , n ) = 2 ( p τ p τ p ) ,
tan τ p = [ ( n 2 1 ) / ( p 2 n 2 ) ] 1 / 2 , tan τ p = [ p 2 ( n 2 1 ) / ( p 2 n 2 ) ] 1 / 2 .
θ max ( p , n ) θ 0 ( p , n ) = 1.087376 ( h π 2 / 12 ) 1 / 3 x 2 / 3 , θ min ( p , n ) θ 0 ( p , n ) = h 1 / 3 ( 9 π / 8 ) 2 / 3 x 2 / 3 ,

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