Advertisement

Abstract

Early one morning in 1735, a small group of people were gathered on top of a mountain in the Peruvian Andes. They belonged to a French scientific expedition, led by Bouguer and La Condamine, that had been sent out to measure a degree of longitude; a Spanish captain named Antonio de Ulloa accompanied them. What they saw on this occasion was, according to Bouguer [1]9 “a phenomenon which must be as old as the world, but which no one seems to have observed so far… A cloud that covered us dissolved itself and let through the rays of the rising sun… Then each of us saw his shadow projected upon the cloud… The closeness of the shadow allowed all its parts to be distinguished: arms, legs, the head. What seemed most remarkable to us was the appearance of a halo or glory around the head, consisting of three or four small concentric circles, very brightly colored, each of them with the same colors as the primary rainbow, with red outermost…”. Ulloa, who gave a similar decription and also drew a picture of what he observed, added: “The most surprising thing was that, of the six or seven people that were present, each one saw the phenomenon only around the shadow of his own head, and saw nothing around other people’s heads…”

Keywords

Surface Wave Edge Domain Multiple Internal Reflection Shadow Side Geometrical Resonance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References and Footnotes

  1. 1.
    J. M. Pernter and F. M. Exner, “Meteorologische Optik”,(W. Braumiiller, Vienna, 1910).Google Scholar
  2. 2.
    A. Hayter “A Voyage in Vain: Coleridge’s Journey to Malta in 1804”,(Faber and Faber, London, 1973). We are indebted to Professor J. B. French for this reference.Google Scholar
  3. 3.
    “The Autobiography of Benvenuto Cellini”,(Brentano’s, New York, 1906), Chapter 128.Google Scholar
  4. 4.
    R. A. R. Tricker, “Introduction to Meteorological Optics”,( American Elsevier Publishing Co., New York, 1970).Google Scholar
  5. 5.
    J. C. Brandt, Publ. Astron. Soc. Pacific 80, 25(1968)CrossRefGoogle Scholar
  6. H. C. Bryant and N. Jarmie, Scient. Amer., 231, 60(July 1974).CrossRefGoogle Scholar
  7. 6.
    C. T. R. Wilson, Nobel Prize Lecture(1927).Google Scholar
  8. 7.
    H. C. Van de Hulst, “Light Scattering by Small Particles”,( John Wiley and Sons, New York, 1957).Google Scholar
  9. 8.
    G. Mie, Ann. Physik, 25, 377(1908).CrossRefGoogle Scholar
  10. 9.
    V. Khare and H. M. Nussenzveig,(to be published).Google Scholar
  11. 10.
    B. Ray, Nature 111, 183(1923).CrossRefGoogle Scholar
  12. 11.
    H. M. Nussenzveig, J. Math. Phys., 10, 82, 125(1969).CrossRefGoogle Scholar
  13. 12.
    H. C. Bryant and A. J. Cox, J. Opt. Soc. Am., 56, 1529(1966).CrossRefGoogle Scholar
  14. 13.
    J. Bricard, Ann. Physique 14, 148(1940)Google Scholar
  15. J. Bricard, Handb. d. Phys., 48, 351,( Springer-Verlag, Berlin, 1957).Google Scholar
  16. 14.
    H. Bucerius, Optik, 1, 188(1946).Google Scholar
  17. 15.
    H. C. Van de Hulst, J. Opt. Soc. Am., 37, 16(1947); see also ref. 7.CrossRefGoogle Scholar
  18. 16.
    H. Ott, Ann. Physik, 41, 443(1942); 4, 432(1948).Google Scholar
  19. 17.
    T. S. Fahlen and H. C. Bryant, J. Opt. Soc. Am., 58, 304(1968).CrossRefGoogle Scholar
  20. 18.
    J. V. Dave, Appl. Opt., 8, 155(1969).CrossRefGoogle Scholar
  21. 19.
    M. J. Saunders, J. Opt. Soc. Am., 60, 1359(1970).Google Scholar
  22. 20.
    For the early history of this subject, see N. A. Logan Proc. IEEE, 53, 773(1965).CrossRefGoogle Scholar
  23. 21.
    V. A. Fock, “Diffraction of Radio Waves Around the Earth’s Surface”,( Publishers of the USSR Academy of Sciences, Moscow, 1946).Google Scholar
  24. 22.
    H. Bremmer, “Terrestrial Radio Waves”,( Elsevier, New York, 1949).Google Scholar
  25. 23.
    B. Van der Pol and H. Bremmer, Phil. Mag., 24, 141, 825(1937).Google Scholar
  26. 24.
    W. Franz, “Theorie der Beugung Elektromagnetischer Wellen”,( Springer-Verlag, Berlin, 1957).Google Scholar
  27. 25.
    S. I. Rubinow, Ann. Phys.(N.Y.) 14, 305(1961).CrossRefGoogle Scholar
  28. 26.
    H. M. Nussenzveig, Ann. Phys.(N.Y.) 34, 23(1965).CrossRefGoogle Scholar
  29. 27.
    V. Khare, Ph.D. Thesis, University of Rochester(1975)Google Scholar
  30. V. Khare and H. M. Nussenzveig,(to be published).Google Scholar
  31. 28.
    V. Khare and H. M. Nussenzveig, Phys. Rev. Lett., 33, 976(1974).CrossRefGoogle Scholar
  32. 29.
    H. M. Nussenzveig, in “Methods and Problems of Theoret ical Physics”, J. E. Bowcock ed.,( North-Holland Publishing Co., Amsterdam, 1970), p. 203.Google Scholar
  33. 30.
    E. C. Titchmarsh, “Introduction to the Theory of Fourier Integrals”, 2nd ed.,(Oxford University Press 1937), p. 60.Google Scholar
  34. 31.
    M. V. Berry and K. E. Mount, Rep. Prog. Phys., 35, 315(1972).CrossRefGoogle Scholar
  35. 32.
    J. B. Keller, in Proc. Symp. Appl. Math., Vol. 8, L. M. Graves ed.,(McGraw-Hill, New York, 1958), p. 27.Google Scholar
  36. 33.
    P. J. Debye, Physik. Z., 9, 775(1908).Google Scholar
  37. 34.
    K. W. Ford, D. L. Hill, M. Wakano and J. A. Wheeler, Ann. Phys.(N.Y.) 7, 239(1959).CrossRefGoogle Scholar
  38. 35.
    C. Chester, B. Friedman and F. Ursell, Proc. Camb. Phil. Soc., 53, 599(1957)CrossRefGoogle Scholar
  39. F. Ursell, Proc. Camb. Phil. Soc., 61, 113(1965).CrossRefGoogle Scholar
  40. 36.
    H. M. Nussenzveig, Scient. Amer., 236, 116(April 1977)CrossRefGoogle Scholar
  41. 37.
    T. S. Fahlen and H. C. Bryant, J. Opt. Soc. Am., 56, 1635(1966).CrossRefGoogle Scholar
  42. 38.
    A. Sommerfeld, “Optics”,( Academic Press Inc., New York, 1954), p. 262.Google Scholar
  43. 39.
    The direct-reflection term p = 0 is omitted in all curves. This does not affect the comparison.Google Scholar
  44. 40.
    P. Walstra, Proc. Koninkl. Akad. Wetensch., B67, 491(1964).Google Scholar
  45. 41.
    M. A. D. Fluendy and K. P. Lawley, “Chemical Applications of Molecular Beam Scattering”,( Chapman and Hall, London, 1973).Google Scholar
  46. 42.
    M. V. Berry, J. Phys., B2, 381(1969).Google Scholar
  47. 43.
    H. L. Harney, P. Braun-Munzinger and C. K. Gelbke, eds. “Classical and Quantum-Mechanical Aspects of Heavy- Ion Collisions”,(Springer-Verlag, Berlin, 1975); cf. specially the contributions by W. E. Frahn and K. W. McVoy and the references quoted therein.Google Scholar
  48. 44.
    W. H. Miller, Adv. Chem. Phys., 25, 63(1974)Google Scholar
  49. T. F. George and J. Ross, Ann. Rev. Phys. Chem., 24, 263(1973).CrossRefGoogle Scholar
  50. 45.
    C. G. Callan, Jr., R. F. Dashen and D. J. Gross, Phys. Lett., 63B, 334(1976).Google Scholar

Copyright information

© Plenum Press, New York 1977

Authors and Affiliations

  • V. Khare
    • 1
  • H. M. Nussenzveig
    • 2
  1. 1.Max-Planck-Institut für StrömungsforschungGöttingenWest Germany
  2. 2.Instituto de FísicaUniversidade de São PauloSão PauloBrazil

Personalised recommendations