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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 66, Iss. 8 — Aug. 1, 1976
  • pp: 768–772

An analytic theory of certain halo arcs

Richard White  »View Author Affiliations

JOSA, Vol. 66, Issue 8, pp. 768-772 (1976)

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A radiance formula shows that the halo arcs produced by ice crystals with two degrees of rotational freedom, the "tangent arcs," are loci on which a mathematical function, the Jacobian, is zero. This enables complete analytic theories of many halo arcs to be given. In other cases, points of contact with the circular halos, and intersections with the solar vertical and parhelic circle, can be found analytically, giving a qualitative description of the forms of the arcs.

© 1976 Optical Society of America

Richard White, "An analytic theory of certain halo arcs," J. Opt. Soc. Am. 66, 768-772 (1976)

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  1. W. J. Humphreys, Physics of the Air (Dover, New York, 1964).
  2. M. Minnaert, Light and Colour in the Open Air (Bell, London, 1952).
  3. C. S. Hastings, "A General Theory of Halos," Mon. Weath. Rev. 48, 322–330 (1920).
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  5. G. A. Gibson, Advanced Calculus (MacMillan, London, 1931), Eq. (3), p. 138.
  6. A. Bravais, "Memoire sur les halos," J. l'Ecole R. Polytech. 18, (31), 1–270 (1847).
  7. H. S. Uhler, "On the deviation produced by prisms," Am. J. Sci. Ser. 4 35, 389–423 (1913).
  8. E. C. W. Goldie, "A graphical guide to halos," Weather 26, 391–393 (1971).
  9. E. C. W. Goldie and J. M. Heighes, "The Berkshire Halo Display of 11 May 1965," Weather 23, 61–69 (1968).
  10. Measured from the source vertical.

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