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Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Vol. 15, Iss. 11 — Nov. 1, 1998
  • pp: 2782–2787

Observation of high-order rainbows formed by a pendant drop

P. H. Ng, M. Y. Tse, and W. K. Lee  »View Author Affiliations


JOSA B, Vol. 15, Issue 11, pp. 2782-2787 (1998)
http://dx.doi.org/10.1364/JOSAB.15.002782


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Abstract

High-order rainbows, up to the 200th order, formed by a pendant water drop and a 50-mW laser beam, have been observed. Some of the characteristics of the high-order rainbows, including angular intensity distributions and angular positions, are reported. Rainbow intensity as a function of order number is also presented. Rainbows beyond the 32nd order have been observed for the first time to our knowledge. Experimental and theoretical results are in reasonable agreement.

© 1998 Optical Society of America

OCIS Codes
(010.1290) Atmospheric and oceanic optics : Atmospheric optics
(010.7340) Atmospheric and oceanic optics : Water
(080.2730) Geometric optics : Matrix methods in paraxial optics

Citation
P. H. Ng, M. Y. Tse, and W. K. Lee, "Observation of high-order rainbows formed by a pendant drop," J. Opt. Soc. Am. B 15, 2782-2787 (1998)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-15-11-2782


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References

  1. H. M. Nussenzveig, “The theory of the rainbow,” Sci. Am. 236, 116–127 (1977). [CrossRef]
  2. K. Sassen, “Angular scattering and rainbow formation in pendant drops,” J. Opt. Soc. Am. 69, 1083–1089 (1979). [CrossRef]
  3. J. Walker, “Multiple rainbows from single drops of water and other liquids,” Am. J. Phys. 44, 421–433 (1976); “How to create and observe a dozen rainbows in a single drop of water,” Sci. Am. 237(7), 138–144 (1977). [CrossRef]
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  12. 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]
  13. For each rainbow between the 18th and the 21st orders, two supernumerary arcs were visible. The supernumerary arcs of the 18th-order rainbow do not show up in the picture because the 5th- and the 18th-order rainbows were attentuated by ~100 times to avoid saturation of the CCD camera.
  14. With our experimental configuration, the 1st-order rainbow cannot be formed, in the sense that there is only a bright patch without a principal peak or supernumerary arc features near the position of the 1st-order rainbow; (p−1)= 1 refers to this bright patch. The (p−1)+13n empirical rule is an accident of the choice of droplet size and the refractive index of water between the red and blue regions (values of roughly 1.332–1.338). By simple geometric optics calculation, one finds that 13n will be replaced by 12n and 14n for refractive-index values of ~1.413 and 1.279, respectively.
  15. We found the peak intensity by integrating the gray-scale values of all pixels within a small portion (~1° of the scattering angle) of the peak region of the rainbow image.
  16. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  17. W. J. Humphreys, Physics of The Air (Dover, New York, 1964).
  18. G(12) is not observable because it is roughly located at the forward scattering direction and is thus masked by the intense scattered light there.

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