Abstract

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

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References

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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).
  4. R. G. Greenler and A. J. Mallman, "Circumscribed Halos," Science 176, 128–131 (1972).
  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.

1972 (1)

R. G. Greenler and A. J. Mallman, "Circumscribed Halos," Science 176, 128–131 (1972).

1971 (1)

E. C. W. Goldie, "A graphical guide to halos," Weather 26, 391–393 (1971).

1968 (1)

E. C. W. Goldie and J. M. Heighes, "The Berkshire Halo Display of 11 May 1965," Weather 23, 61–69 (1968).

1920 (1)

C. S. Hastings, "A General Theory of Halos," Mon. Weath. Rev. 48, 322–330 (1920).

1913 (1)

H. S. Uhler, "On the deviation produced by prisms," Am. J. Sci. Ser. 4 35, 389–423 (1913).

1847 (1)

A. Bravais, "Memoire sur les halos," J. l'Ecole R. Polytech. 18, (31), 1–270 (1847).

Bravais, A.

A. Bravais, "Memoire sur les halos," J. l'Ecole R. Polytech. 18, (31), 1–270 (1847).

Gibson, G. A.

G. A. Gibson, Advanced Calculus (MacMillan, London, 1931), Eq. (3), p. 138.

Goldie, E. C. W.

E. C. W. Goldie, "A graphical guide to halos," Weather 26, 391–393 (1971).

E. C. W. Goldie and J. M. Heighes, "The Berkshire Halo Display of 11 May 1965," Weather 23, 61–69 (1968).

Greenler, R. G.

R. G. Greenler and A. J. Mallman, "Circumscribed Halos," Science 176, 128–131 (1972).

Hastings, C. S.

C. S. Hastings, "A General Theory of Halos," Mon. Weath. Rev. 48, 322–330 (1920).

Heighes, J. M.

E. C. W. Goldie and J. M. Heighes, "The Berkshire Halo Display of 11 May 1965," Weather 23, 61–69 (1968).

Humphreys, W. J.

W. J. Humphreys, Physics of the Air (Dover, New York, 1964).

Mallman, A. J.

R. G. Greenler and A. J. Mallman, "Circumscribed Halos," Science 176, 128–131 (1972).

Minnaert, M.

M. Minnaert, Light and Colour in the Open Air (Bell, London, 1952).

Uhler, H. S.

H. S. Uhler, "On the deviation produced by prisms," Am. J. Sci. Ser. 4 35, 389–423 (1913).

Am. J. Sci. Ser. (1)

H. S. Uhler, "On the deviation produced by prisms," Am. J. Sci. Ser. 4 35, 389–423 (1913).

J. l'Ecole R. Polytech. (1)

A. Bravais, "Memoire sur les halos," J. l'Ecole R. Polytech. 18, (31), 1–270 (1847).

Mon. Weath. Rev. (1)

C. S. Hastings, "A General Theory of Halos," Mon. Weath. Rev. 48, 322–330 (1920).

Science (1)

R. G. Greenler and A. J. Mallman, "Circumscribed Halos," Science 176, 128–131 (1972).

Weather (2)

E. C. W. Goldie, "A graphical guide to halos," Weather 26, 391–393 (1971).

E. C. W. Goldie and J. M. Heighes, "The Berkshire Halo Display of 11 May 1965," Weather 23, 61–69 (1968).

Other (4)

Measured from the source vertical.

G. A. Gibson, Advanced Calculus (MacMillan, London, 1931), Eq. (3), p. 138.

W. J. Humphreys, Physics of the Air (Dover, New York, 1964).

M. Minnaert, Light and Colour in the Open Air (Bell, London, 1952).

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