OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 37, Iss. 9 — Mar. 20, 1998
  • pp: 1540–1550

Rainbow scattering by a cylinder with a nearly elliptical cross section

Charles L. Adler, James A. Lock, and Bradley R. Stone  »View Author Affiliations


Applied Optics, Vol. 37, Issue 9, pp. 1540-1550 (1998)
http://dx.doi.org/10.1364/AO.37.001540


View Full Text Article

Enhanced HTML    Acrobat PDF (235 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We both theoretically and experimentally examine the behavior of the first- and the second-order rainbows produced by a normally illuminated glass rod, which has a nearly elliptical cross section, as it is rotated about its major axis. We decompose the measured rainbow angle, taken as a function of the rod’s rotation angle, into a Fourier series and find that the rod’s refractive index, average ellipticity, and deviation from ellipticity are encoded primarily in the m = 0, 2, 3 Fourier coefficients, respectively. We determine these parameters for our glass rod and, where possible, compare them with independent measurements. We find that the average ellipticity of the rod agrees well with direct measurements, but that the rod’s diameter inferred from the spacing of the supernumeraries of the first-order rainbow is significantly larger than that obtained by direct measurement. We also determine the conditions under which the deviation of falling water droplets from an oblate spheroidal shape permits the first few supernumeraries of the second-order rainbow to be observed in a rain shower.

© 1998 Optical Society of America

OCIS Codes
(010.1310) Atmospheric and oceanic optics : Atmospheric scattering
(080.1510) Geometric optics : Propagation methods
(290.3030) Scattering : Index measurements
(290.5820) Scattering : Scattering measurements

History
Original Manuscript: June 20, 1997
Revised Manuscript: November 12, 1997
Published: March 20, 1998

Citation
Charles L. Adler, James A. Lock, and Bradley R. Stone, "Rainbow scattering by a cylinder with a nearly elliptical cross section," Appl. Opt. 37, 1540-1550 (1998)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-37-9-1540


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. C. B. Boyer, The Rainbow From Myth to Mathematics (Princeton U. Press, Princeton, N.J., 1987), p. 309.
  2. W. Möbius, “Zur Theorie des Regenbogens und ihrer experimentallen Prüfung,” Abh. Kgl. Saechs. Ges. Wiss. Math.-Phys. Kl. 30, 105–254 (1907–1909).
  3. W. Möbius, “Zur Theorie des Regenbogens und ihrer experimentallen Prüfung,” Ann. Phys. 33, 1493–1558 (1910). [CrossRef]
  4. H. M. Presby, “Refractive index and diameter measurements of unclad optical fibers,” J. Opt. Soc. Am. 64, 280–284 (1974). [CrossRef]
  5. J. A. Lock, C. L. Adler, “Debye-series analysis of the first-order rainbow produced in scattering of a diagonally incident plane wave by a circular cylinder,” J. Opt. Soc. Am. A 14, 1316–1328 (1997). [CrossRef]
  6. P. L. Marston, “Descartes glare points in scattering by icicles: color photographs and a tilted dielectric cylinder model of caustic and glare-point evolution,” Appl. Opt. 37, 1551–1556 (1998). [CrossRef]
  7. C. M. Mount, D. B. Thiessen, P. L. Marston, “Scattering observations for tilted transparent fibers: evolution of Airy caustics with cylinder tilt and the caustic-merging transition,” Appl. Opt. 37, 1534–1539 (1998). [CrossRef]
  8. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), pp. 297–328.
  9. J. A. Lock, “Scattering of a diagonally incident focused Gaussian beam by an infinitely long homogeneous circular cylinder,” J. Opt. Soc. Am. A 14, 640–652 (1997). [CrossRef]
  10. G. Gouesbet, “Scattering of a first order Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation,” Part. Part. Syst. Charact. 12, 242–256 (1995). [CrossRef]
  11. P. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), pp. 1407–1423.
  12. J. J. Bowman, T. B. A. Senior, P. L. E. Uslenghi, Electromagnetic and Acoustic Scattering by Simple Shapes (Hemisphere, New York, 1987), pp. 129–180.
  13. J. P. Barton, “Electromagnetic-field calculations for irregularly shaped, layered cylindrical particles with focused illumination,” Appl. Opt. 36, 1312–1319 (1997). [CrossRef] [PubMed]
  14. H. R. Pruppacher, R. L. Pitter, “A semi-empirical determination of the shape of cloud and rain droplets,” J. Atmos. Sci. 28, 86–94 (1971). [CrossRef]
  15. A. B. Fraser, “Why can the supernumerary bows be seen in a rain shower?” J. Opt. Soc. Am. 73, 1626–1628 (1983). [CrossRef]
  16. G. P. Können, “Appearance of supernumeraries of the secondary bow in rain showers,” J. Opt. Soc. Am. A 4, 810–816 (1987). [CrossRef]
  17. S. D. Gedzelman, “Rainbows in strong vertical atmospheric fields,” J. Opt. Soc. Am. A 5, 1717–1721 (1988). [CrossRef]
  18. D. Marcuse, “Light scattering from elliptical fibers,” Appl. Opt. 13, 1903–1905 (1974). [CrossRef] [PubMed]
  19. C. L. Adler, J. A. Lock, B. R. Stone, C. J. Garcia, “High-order interior caustics produced in scattering of a diagonally incident plane wave by a circular cylinder,” J. Opt. Soc. Am. A 14, 1305–1315 (1997). [CrossRef]
  20. J. A. Lock, T. A. McCollum, “Further thoughts on Newton’s zero-order rainbow,” Am. J. Phys. 62, 1082–1089 (1994). [CrossRef]
  21. P. L. Marston, “Rainbow phenomena and the detection of nonsphericity in drops,” Appl. Opt. 19, 680–685 (1980). [CrossRef] [PubMed]
  22. E. A. Hovenac, J. A. Lock, “Assessing the contributions of surface waves and complex rays to far-field Mie scattering by use of the Debye series,” J. Opt. Soc. Am. A 9, 781–795 (1992). [CrossRef]
  23. K. Sassen, “Angular scattering and rainbow formation in pendant drops,” J. Opt. Soc. Am. 69, 1083–1089 (1979). [CrossRef]
  24. J. A. Lock, C. L. Adler, B. R. Stone, P. D. Zajak, “Amplification of high-order rainbows of a cylinder with an elliptical cross section,” Appl. Opt. 37, 1527–1533 (1998). [CrossRef]
  25. M. Minnaert, Light and Colour in the Open Air (Dover, New York, 1954), p. 173.
  26. R. Greenler, Rainbows, Halos, and Glories (Cambridge U. Press, Cambridge, 1989), p. 20.
  27. A. W. Green, “An approximation for the shapes of large raindrops,” J. Appl. Meteorol. 14, 1578–1583 (1975). [CrossRef]
  28. H. R. Pruppacher, J. D. Klett, Microphysics of Clouds and Precipitation (Reidel, Dordrecht, The Netherlands, 1978), pp. 23–25.
  29. A. B. Fraser, “Chasing rainbows,” Weatherwise 36, 280–289 (1983). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited