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Rainbows, Coronas and Glories

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The Mie Theory

Part of the book series: Springer Series in Optical Sciences ((SSOS,volume 169))

Abstract

Rainbows, coronas and glories are examples of atmospheric optical phenomena caused by the scattering of sunlight from spherical drops of water. It is surprising that the apparently simple process of scattering of light by spherical drops of water can result in this wide range of colourful effects. However, the scattering mechanisms are very complicated. Eminent scientists (such as Descartes, Newton, Young, Airy and many others) offered various explanations for the formation of rainbows—thus making major contributions to our understanding of the nature of light. The basic features of rainbows can be explained by geometrical optics but, in the early 1800s, supernumerary arcs on rainbows provided crucial supporting evidence for the wave theory of light. In 1908, Mie provided a rigorous (but very complicated) solution to the problem of scattering of light by spherical particles. More than 100 years later, Mie’s solution can now be used to produce excellent full-colour simulations. Examples of such simulations show how the appearance of these phenomena vary with the size of the water drops, as well as describing the scattering mechanisms that are responsible for their formation.

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Notes

  1. 1.

    Such equations are frequently attributed to Fraunhofer, but Craig Bohren has pointed out in a private communication that, without diminishing the importance of Fraunhofer’s pioneering work in experimental optics, there is no evidence to suggest that Fraunhofer developed any theoretical treatment of diffraction. Consequently, Fresnel-Fraunhofer-Airy-Schwerd might be a more appropriate designation. Schwerd’s contribution is described in [22].

References

  1. J.A. Adam, The mathematical physics of rainbows and glories. Phys. Rep. 356, 229–365 (2002)

    Article  ADS  MATH  Google Scholar 

  2. J.A. Adam, Geometric optics and rainbows: generalization of a result by Huygens. Appl. Opt. 47, H11–H13 (2008)

    Article  ADS  Google Scholar 

  3. G.B. Airy, On the intensity of light in the neighbourhood of a caustic. Trans. Camb. Philos. Soc. 6, 397–403 (1838)

    Google Scholar 

  4. H. Bech, A. Leder, Particle sizing by ultrashort laser pulses–numerical simulation. Optik 115, 205–217 (2004)

    Article  ADS  Google Scholar 

  5. H. Bech, A. Leder, Particle sizing by time-resolved Mie calculations—A numerical study. Optik 117, 40–47 (2006)

    Article  ADS  Google Scholar 

  6. C.F. Bohren, D.R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983)

    Google Scholar 

  7. C.B. Boyer, The Rainbow: From Myth to Mathematics. (Princeton University, Princeton, 1987), reprint of 1959 Thomas Yoseloff edn

    Google Scholar 

  8. H.C. Bryant, A.J. Cox, Mie theory and the glory. J. Opt. Soc. Am. 56, 1529–1532 (1966)

    Article  ADS  Google Scholar 

  9. H.C. Bryant, N. Jarmie, The glory. Sci. Am. 231, 60–71 (1974)

    Article  ADS  Google Scholar 

  10. L. Cowley, P. Laven, M. Vollmer, Rings around the sun and moon: coronae and diffraction. Phys. Educ. 41, 51–59 (2005)

    Article  ADS  Google Scholar 

  11. Iris software http://www.atoptics.co.uk/droplets/iris.htm. (Cited 31 October 2009)

  12. J.V. Dave, Scattering of visible light by large water spheres. Appl. Opt. 8, 155–164 (1969)

    Article  ADS  Google Scholar 

  13. P. Debye, Das elektromagnetische Feld um einen Zylinder und die Theorie des Regenbogens. Physikalische Zeitschrift 9, 775–778 (1908) [N.B. An English translation of this paper entitled The electromagnetic field around a cylinder and the theory of the rainbow is available in Selected Papers on Geometrical Aspects of Scattering, SPIE Milestone Series Volume MS 89 (1993)]

    Google Scholar 

  14. T.S. Fahlen, H.C. Bryant, Direct observation of surface waves on droplets. J. Opt. Soc. Am. 56, 1635–1636 (1966)

    Article  Google Scholar 

  15. S.D. Gedzelman, Simulating glories and cloudbows in color. Appl. Opt. 42, 429–435 (2003)

    Article  ADS  Google Scholar 

  16. S.D. Gedzelman, Simulating rainbows in their atmospheric environment. Appl. Opt. 47, H176–H181 (2008)

    Article  Google Scholar 

  17. S.D. Gedzelman, Simulating halos and coronas in their atmospheric environment. Appl. Opt. 47, H157–H166 (2008)

    Article  ADS  Google Scholar 

  18. S.D. Gedzelman, J.A. Lock, Simulating Coronas in Color. Appl. Opt. 42, 497–504 (2003)

    Article  ADS  Google Scholar 

  19. G. Gouesbet, B. Maheu, G. Grehan, Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formalism. J. Opt. Soc. Am. A 5, 1427–1443 (1988)

    Article  MathSciNet  ADS  Google Scholar 

  20. W.T. Grandy, Scattering of Waves from Large Spheres (Cambridge University, Cambridge, 2001)

    Google Scholar 

  21. R. Greenler, Rainbows (Halos and Glories. Cambridge University, Cambridge, 1980)

    Google Scholar 

  22. R.B. Hoover, F.S. Harris, Die Beugungserscheinungen: a Tribute to F. M. Schwerd’s Monumental Work on Fraunhofer Diffraction. Appl. Opt. 8, 2161–2164 (1969)

    Article  ADS  Google Scholar 

  23. 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)

    Article  ADS  Google Scholar 

  24. H. Inada, New calculation of surface wave contributions associated with Mie backscattering. Appl. Opt. 12, 1516–1523 (1973)

    Article  ADS  Google Scholar 

  25. V. Khare, Short-wavelength scattering of electromagnetic waves by a homogeneous dielectric sphere. Ph.D. thesis (University of Rochester, Rochester, 1976). This reference may not be readily available, but the calculation method is summarized in 23

    Google Scholar 

  26. V. Khare, H.M. Nussenzveig, Theory of the glory. Phys. Rev. Lett. 38, 1279–1282 (1977)

    Article  ADS  Google Scholar 

  27. G.P. Können, J.H. de Boer, Polarized rainbow. Appl. Opt. 18, 1961–1965 (1979)

    Article  ADS  Google Scholar 

  28. G.P. Können, Polarized light in nature (Cambridge University Press, Cambridge, 1985)

    Google Scholar 

  29. P. Laven, Simulation of rainbows, coronas, and glories by use of Mie theory. Appl. Opt. 42, 436–444 (2003)

    Article  ADS  Google Scholar 

  30. P. Laven, Simulation of rainbows, coronas and glories using Mie theory and the Debye series. J. Quant. Spectrosc. Radiat. Transf. 89, 257–269 (2004)

    Article  ADS  Google Scholar 

  31. P. Laven, How are glories formed? Appl. Opt. 44, 5675–5683 (2005)

    Article  ADS  Google Scholar 

  32. P. Laven, Atmospheric glories: simulations and observations. Appl. Opt. 44, 5667–5674 (2005)

    Article  ADS  Google Scholar 

  33. P. Laven, Noncircular glories and their relationship to cloud droplet size. Appl. Opt. 47, H25–H30 (2008)

    Article  ADS  Google Scholar 

  34. P. Laven, Effects of refractive index on glories. Appl. Opt. 47, H133–H142 (2008)

    Article  ADS  Google Scholar 

  35. MiePlot software, http://www.philiplaven.com/MiePlot.htm (Cited 31 October 2009)

  36. R.L. Lee, Mie theory, Airy theory, and the natural rainbow. Appl. Opt. 37, 1506–1519 (1998)

    Article  ADS  Google Scholar 

  37. R.L. Lee, A.B. Fraser, The Rainbow Bridge: Rainbows in Art, Myth and Science (Pennsylvania State University Press, Pennsylvania, 2001)

    Google Scholar 

  38. J.A. Lock, L. Yang, Mie theory model of the corona. Appl. Opt. 30, 3408–3414 (1991)

    Article  ADS  Google Scholar 

  39. J.A. Lock, Contribution of high-order rainbows to the scattering of a Gaussian laser beam by a spherical particle. J. Opt. Soc. Am. A 10, 693–706 (1993)

    Article  ADS  Google Scholar 

  40. J.A. Lock, Improved Gaussian beam-scattering algorithm. Appl. Opt. 34, 559–570 (1995)

    Article  ADS  Google Scholar 

  41. J.A. Lock, Role of the tunneling ray in near-critical-angle scattering by a dielectric sphere. J. Opt. Soc. Am. A 20, 499–507 (2003)

    Article  ADS  Google Scholar 

  42. J.A. Lock, G. Gouesbet, Generalized Lorenz—Mie theory and applications. J. Quant. Spectrosc. Radiat. Transf. 110, 800–807 (2009)

    Article  ADS  Google Scholar 

  43. D.K. Lynch, W. Livingston, Color and Light in Nature (Cambridge University, Cambridge, 2001)

    Google Scholar 

  44. L. Méès, G. Gouesbet, G. Gréhan, Time-resolved scattering diagrams for a sphere illuminated by plane wave and focused short pulses. Opt. Commun. 194, 59–65 (2001)

    Article  ADS  Google Scholar 

  45. L. Méès, G. Gouesbet, G. Gréhan, Scattering of Laser Pulses (Plane Wave and Focused Gaussian Beam) by Spheres. Appl. Opt. 40, 2546–2550 (2001)

    Article  ADS  Google Scholar 

  46. G. Mie, Beitrage zur Optik trüber Medien, speziell kolloidaler Metallosungen. Ann. Phys. Leipzig 25, 377–445 (1908)

    Article  ADS  MATH  Google Scholar 

  47. M. Minnaert, The Nature of Light and Colour in the Open Air (Dover Publications, New York, 1954)

    Google Scholar 

  48. H.M. Nussenzveig, High-frequency scattering by a transparent sphere. I. Direct reflection and transmission. J. Math. Phys. 10, 82–124 (1969)

    Article  MathSciNet  ADS  Google Scholar 

  49. H.M. Nussenzveig, High-frequency scattering by a transparent sphere. II. Theory of the rainbow and the glory. J. Math. Phys. 10, 125–176 (1969)

    Article  MathSciNet  ADS  Google Scholar 

  50. H.M. Nussenzveig, Complex angular momentum theory of the rainbow and the glory. J. Opt. Soc. Am. 69, 1068–1079 (1979)

    Article  MathSciNet  ADS  Google Scholar 

  51. H.M. Nussenzveig, Diffraction Effects in Semiclassical Scattering (Cambridge University, Cambridge, 1992)

    Book  Google Scholar 

  52. H.M. Nussenzveig, Does the glory have a simple explanation? Opt. Lett. 27, 1379–1381 (2002)

    Article  ADS  Google Scholar 

  53. H.M. Nussenzveig, Light tunneling in clouds. Appl. Opt. 42, 1588–1593 (2003)

    Article  ADS  Google Scholar 

  54. J.A. Shaw, P.J. Neiman, Coronas and iridescence in mountain wave clouds. Appl. Opt. 42, 476–485 (2003)

    Article  ADS  Google Scholar 

  55. R.A.R. Tricker, Introduction to Meteorological Optics (American-Elsevier, New York, 1970)

    Google Scholar 

  56. H.C. van de Hulst, A theory of the anti-coronae. J. Opt. Soc. Am. 37, 16–22 (1947)

    Article  ADS  Google Scholar 

  57. H.C. van de Hulst, Light Scattering by Small Particles ( Dover, New York, 1981), reprint of 1957 Wiley edition

    Google Scholar 

  58. M. Vollmer, Effects of absorbing particles on coronas and glories. Appl. Opt. 44, 5658–5666 (2005)

    Article  ADS  Google Scholar 

  59. M. Vollmer, Lichtspiele in der Luft (Elsevier, München, 2006)

    Google Scholar 

  60. R.T. Wang, H.C. van de Hulst, Rainbows: Mie computations and the Airy approximation. Appl. Opt. 30, 106–117 (1991)

    Article  ADS  Google Scholar 

  61. T. Young, Experiments and calculations relative to physical optics. A Bakerian Lecture read on November 24, 1803. Phil. Trans. Roy. Soc. 1–16 (1804)

    Google Scholar 

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Authors and Affiliations

  1. 9 Russells Crescent, Horley, RH6 7DJ, UK

    Philip Laven

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  1. Philip Laven
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Correspondence to Philip Laven .

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  1. Halle-Wittenberg, Fakultät für Naturwissenschaften II, Martin-Luther-Universität, Von-Seckendorff-Platz 1, Halle/Saale, 06120, Germany

    Wolfram Hergert

  2. Stiftung Institut für Werkstofftechnik, Badgasteiner Str. 3, Bremen, 28359, Germany

    Thomas Wriedt

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Laven, P. (2012). Rainbows, Coronas and Glories. In: Hergert, W., Wriedt, T. (eds) The Mie Theory. Springer Series in Optical Sciences, vol 169. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28738-1_7

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  • DOI: https://doi.org/10.1007/978-3-642-28738-1_7

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