Abstract

We have studied the seldom-seen halo phenomenon that can arise in divergent light, Minnaert’s Cigar, which we produced in laboratory experiments and computer simulation. In the laboratory experiments halos or transections were produced in clouds of alum crystals precipitated in a solution of ethyl alcohol or in alum crystals deposited upon glass plates. The three-dimensional cigar form was less pronounced in our small-scale experiments than when the form was observed over several meters. In our experiments and simulations transections through Minnaert’s Cigar include different halo forms that may arise on window panes or windshields covered with halo-active ice crystals or as horizontal halos on glittering frost-covered ground.

© 2000 Optical Society of America

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References

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  1. C. Floor, “Rainbows and haloes in lighthouse beams,” Weather 35, 203–208 (1980).
    [CrossRef]
  2. C. Floor, “Optic phenomena and optical illusions near lighthouses,” Z. Meteorol. 32, 229–233 (1982).
  3. F. Linke, F. Möller, eds., Physik der Atmosphäre I. Atmosphärische Strahlungsforschung, Vol. 8 of Handbuch der Geophysik (Bornträger, Berlin, 1961).
  4. J. O. Mattsson, S. Nordbeck, B. Rystedt, “Dewbows and fogbows in divergent light,” No. 11 of Lund Studies in Geography Series C (Lund University, Lund, Sweden, 1971).
  5. J. L. Monteith, “Refraction and the spider,” Weather 9, 140–141 (1954).
    [CrossRef]
  6. J. Walker, The Flying Circus of Physics with Answers (Wiley, New York, 1975).
  7. J. O. Mattsson, “Concerning haloes, rainbows and dewbows in divergent light,” Weather 53, 176–181 (1998).
    [CrossRef]
  8. J. O. Mattsson, L. Bärring, “Reflections on retroreflection,” submitted to Meteorol. Z.
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    [CrossRef] [PubMed]
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    [CrossRef]
  11. K. Lenggenhager, “Eine neue Erklärung des Brockengespenstes und seine Nebelglorie,” Arch. Meteorol. Geophys. Bioklimatol. Ser. A 26, 381–392 (1977).
    [CrossRef]
  12. K. Lenggenhager, “Zur immer umstritten Erklärung des Brockengespenstes,” Z. Meteorol. 29, 179–183 (1979).
  13. F. Richarz, “Über Beobachtung des künstlichen Brockengespenstes,” Meteorol. Z. 25, 19–25 (1908).
  14. J. O. Mattsson, “Experiments on the horizontal circle in divergent light,” Z. Meteorol. 28, 123–125 (1978).
  15. J. O. Mattsson, “‘Sun–sun’ and light-pillars of street lamps,” Weather 28, 66–68 (1973).
    [CrossRef]
  16. A. J. Mallmann, J. L. Hock, R. G. Greenler, “Comparison of sun pillars with light pillars from nearby light sources,” Appl. Opt. 37, 1441–1449 (1998).
    [CrossRef]
  17. M. Minnaert, “Een halo in de onmiddellijke nabijheid van het oog,” Hemel Dampkring 26, 51–54 (1928).
  18. M. Minnaert, The Nature of Light and Colour in the Open Air (Dover, New York, 1954); German edition, Light and Color in the Outdoors (Springer-Verlag, Berlin, 1993).
  19. J. O. Mattsson, “Experiments on horizontal haloes in divergent light,” Weather 29, 148–150 (1974).
    [CrossRef]
  20. A. Cornu, “Sur la reproduction artificielle des halos et des cercles parhéliques,” C. R. Acad. Sci. 108, 429–433 (1889).
  21. M. Vollmer, R. Tammer, “Laboratory experiments in atmospheric optics,” Appl. Opt. 37, 1557–1568 (1998).
    [CrossRef]
  22. J. M. Pernter, F. M. Exner, Meteorologische Optik, 2nd ed. (Braumüller, Vienna, 1922).
  23. A. Wegener, “Optik den Atmosphäre,” in Müller–Pouillets Lehrbuch der Physik, 11th ed., A. Eucken, O. Lummer, E. Waetzmann, eds. (Vieweg, Braunschweig, Germany, 1928), Chap. 3.
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    [CrossRef]

1998

1994

1982

C. Floor, “Optic phenomena and optical illusions near lighthouses,” Z. Meteorol. 32, 229–233 (1982).

1980

C. Floor, “Rainbows and haloes in lighthouse beams,” Weather 35, 203–208 (1980).
[CrossRef]

1979

K. Lenggenhager, “Zur immer umstritten Erklärung des Brockengespenstes,” Z. Meteorol. 29, 179–183 (1979).

1978

J. O. Mattsson, “Experiments on the horizontal circle in divergent light,” Z. Meteorol. 28, 123–125 (1978).

1977

K. Lenggenhager, “Eine neue Erklärung des Brockengespenstes und seine Nebelglorie,” Arch. Meteorol. Geophys. Bioklimatol. Ser. A 26, 381–392 (1977).
[CrossRef]

1974

J. O. Mattsson, “Experiments on horizontal haloes in divergent light,” Weather 29, 148–150 (1974).
[CrossRef]

1973

J. O. Mattsson, “‘Sun–sun’ and light-pillars of street lamps,” Weather 28, 66–68 (1973).
[CrossRef]

1954

J. L. Monteith, “Refraction and the spider,” Weather 9, 140–141 (1954).
[CrossRef]

1928

M. Minnaert, “Een halo in de onmiddellijke nabijheid van het oog,” Hemel Dampkring 26, 51–54 (1928).

1908

F. Richarz, “Über Beobachtung des künstlichen Brockengespenstes,” Meteorol. Z. 25, 19–25 (1908).

1891

A. W. Clayden, “On Brocken spectres in a London fog,” Q. J. R. Meteorol. Soc. 17, 209–216 (1891).
[CrossRef]

1889

A. Cornu, “Sur la reproduction artificielle des halos et des cercles parhéliques,” C. R. Acad. Sci. 108, 429–433 (1889).

Bärring, L.

J. O. Mattsson, L. Bärring, “Reflections on retroreflection,” submitted to Meteorol. Z.

Bates, H. E.

Clayden, A. W.

A. W. Clayden, “On Brocken spectres in a London fog,” Q. J. R. Meteorol. Soc. 17, 209–216 (1891).
[CrossRef]

Cornu, A.

A. Cornu, “Sur la reproduction artificielle des halos et des cercles parhéliques,” C. R. Acad. Sci. 108, 429–433 (1889).

Exner, F. M.

J. M. Pernter, F. M. Exner, Meteorologische Optik, 2nd ed. (Braumüller, Vienna, 1922).

Floor, C.

C. Floor, “Optic phenomena and optical illusions near lighthouses,” Z. Meteorol. 32, 229–233 (1982).

C. Floor, “Rainbows and haloes in lighthouse beams,” Weather 35, 203–208 (1980).
[CrossRef]

Fraser, A. B.

Greenler, R. G.

Hock, J. L.

Lenggenhager, K.

K. Lenggenhager, “Zur immer umstritten Erklärung des Brockengespenstes,” Z. Meteorol. 29, 179–183 (1979).

K. Lenggenhager, “Eine neue Erklärung des Brockengespenstes und seine Nebelglorie,” Arch. Meteorol. Geophys. Bioklimatol. Ser. A 26, 381–392 (1977).
[CrossRef]

Mallmann, A. J.

Mattsson, J. O.

J. O. Mattsson, “Concerning haloes, rainbows and dewbows in divergent light,” Weather 53, 176–181 (1998).
[CrossRef]

J. O. Mattsson, “Experiments on the horizontal circle in divergent light,” Z. Meteorol. 28, 123–125 (1978).

J. O. Mattsson, “Experiments on horizontal haloes in divergent light,” Weather 29, 148–150 (1974).
[CrossRef]

J. O. Mattsson, “‘Sun–sun’ and light-pillars of street lamps,” Weather 28, 66–68 (1973).
[CrossRef]

J. O. Mattsson, L. Bärring, “Reflections on retroreflection,” submitted to Meteorol. Z.

J. O. Mattsson, S. Nordbeck, B. Rystedt, “Dewbows and fogbows in divergent light,” No. 11 of Lund Studies in Geography Series C (Lund University, Lund, Sweden, 1971).

Minnaert, M.

M. Minnaert, “Een halo in de onmiddellijke nabijheid van het oog,” Hemel Dampkring 26, 51–54 (1928).

M. Minnaert, The Nature of Light and Colour in the Open Air (Dover, New York, 1954); German edition, Light and Color in the Outdoors (Springer-Verlag, Berlin, 1993).

Monteith, J. L.

J. L. Monteith, “Refraction and the spider,” Weather 9, 140–141 (1954).
[CrossRef]

Nordbeck, S.

J. O. Mattsson, S. Nordbeck, B. Rystedt, “Dewbows and fogbows in divergent light,” No. 11 of Lund Studies in Geography Series C (Lund University, Lund, Sweden, 1971).

Pernter, J. M.

J. M. Pernter, F. M. Exner, Meteorologische Optik, 2nd ed. (Braumüller, Vienna, 1922).

Richarz, F.

F. Richarz, “Über Beobachtung des künstlichen Brockengespenstes,” Meteorol. Z. 25, 19–25 (1908).

Rystedt, B.

J. O. Mattsson, S. Nordbeck, B. Rystedt, “Dewbows and fogbows in divergent light,” No. 11 of Lund Studies in Geography Series C (Lund University, Lund, Sweden, 1971).

Tammer, R.

Vollmer, M.

Walker, J.

J. Walker, The Flying Circus of Physics with Answers (Wiley, New York, 1975).

Warner, G.

Wegener, A.

A. Wegener, “Optik den Atmosphäre,” in Müller–Pouillets Lehrbuch der Physik, 11th ed., A. Eucken, O. Lummer, E. Waetzmann, eds. (Vieweg, Braunschweig, Germany, 1928), Chap. 3.

Appl. Opt.

Arch. Meteorol. Geophys. Bioklimatol. Ser. A

K. Lenggenhager, “Eine neue Erklärung des Brockengespenstes und seine Nebelglorie,” Arch. Meteorol. Geophys. Bioklimatol. Ser. A 26, 381–392 (1977).
[CrossRef]

C. R. Acad. Sci.

A. Cornu, “Sur la reproduction artificielle des halos et des cercles parhéliques,” C. R. Acad. Sci. 108, 429–433 (1889).

Hemel Dampkring

M. Minnaert, “Een halo in de onmiddellijke nabijheid van het oog,” Hemel Dampkring 26, 51–54 (1928).

Meteorol. Z.

F. Richarz, “Über Beobachtung des künstlichen Brockengespenstes,” Meteorol. Z. 25, 19–25 (1908).

Q. J. R. Meteorol. Soc.

A. W. Clayden, “On Brocken spectres in a London fog,” Q. J. R. Meteorol. Soc. 17, 209–216 (1891).
[CrossRef]

Weather

C. Floor, “Rainbows and haloes in lighthouse beams,” Weather 35, 203–208 (1980).
[CrossRef]

J. L. Monteith, “Refraction and the spider,” Weather 9, 140–141 (1954).
[CrossRef]

J. O. Mattsson, “Concerning haloes, rainbows and dewbows in divergent light,” Weather 53, 176–181 (1998).
[CrossRef]

J. O. Mattsson, “‘Sun–sun’ and light-pillars of street lamps,” Weather 28, 66–68 (1973).
[CrossRef]

J. O. Mattsson, “Experiments on horizontal haloes in divergent light,” Weather 29, 148–150 (1974).
[CrossRef]

Z. Meteorol.

C. Floor, “Optic phenomena and optical illusions near lighthouses,” Z. Meteorol. 32, 229–233 (1982).

K. Lenggenhager, “Zur immer umstritten Erklärung des Brockengespenstes,” Z. Meteorol. 29, 179–183 (1979).

J. O. Mattsson, “Experiments on the horizontal circle in divergent light,” Z. Meteorol. 28, 123–125 (1978).

Other

M. Minnaert, The Nature of Light and Colour in the Open Air (Dover, New York, 1954); German edition, Light and Color in the Outdoors (Springer-Verlag, Berlin, 1993).

F. Linke, F. Möller, eds., Physik der Atmosphäre I. Atmosphärische Strahlungsforschung, Vol. 8 of Handbuch der Geophysik (Bornträger, Berlin, 1961).

J. O. Mattsson, S. Nordbeck, B. Rystedt, “Dewbows and fogbows in divergent light,” No. 11 of Lund Studies in Geography Series C (Lund University, Lund, Sweden, 1971).

J. O. Mattsson, L. Bärring, “Reflections on retroreflection,” submitted to Meteorol. Z.

J. Walker, The Flying Circus of Physics with Answers (Wiley, New York, 1975).

J. M. Pernter, F. M. Exner, Meteorologische Optik, 2nd ed. (Braumüller, Vienna, 1922).

A. Wegener, “Optik den Atmosphäre,” in Müller–Pouillets Lehrbuch der Physik, 11th ed., A. Eucken, O. Lummer, E. Waetzmann, eds. (Vieweg, Braunschweig, Germany, 1928), Chap. 3.

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Figures (9)

Fig. 1
Fig. 1

(a) In parallel light, ice crystals that produce a 22° halo define an apparent cone-shaped surface with a vertex angle of ∼44°. (b) In divergent light the actual crystals define the apparent surface of a cigar-shaped body, here named Minnaert’s Cigar. A cone tangential to this surface has a vertex angle of ∼44°. Partly from Ref. 7.

Fig. 2
Fig. 2

9.5° halo formed around a light source seen through a thin glass vessel containing a water solution with precipitated alum crystals when ethyl alcohol was added to the saturated alum solution.

Fig. 3
Fig. 3

Microphotograph of alum crystals upon a glass plate. The average length of the crystals is ∼0.1 mm.

Fig. 4
Fig. 4

Halo rings in an alum-crystal-covered glass plate close to the light source and perpendicular to a line from the light source to the eye (camera). The distance between the plate and the light source was (a) 20 cm, (b) 15 cm, (c) 10 cm, (d) 5 cm. The distance between the plate and the camera was 60 cm. Two outer halo rings are discernable in (b), (c), and (d).

Fig. 5
Fig. 5

(a) In the quadriangular polygon (ABCD) inside the circle, B is the observer’s eye and D is the light source. The sum of the opposing angles in the polygon is always 180°. Therefore the sum of r d and r c is α, which can easily be shown to equal r max. The chord BD is defined to be of unit length, and the radius of the circle is R = 1/2 sinr max. When circular bow BD is rotated about line BD, a cigar-shaped surface is produced. (b) The relationship among the radius of a halo, r d , developed in divergent light on a plane perpendicular to the symmetry axis of Minnaert’s Cigar (the 22° ice halo); the distance between the light source and the center of this halo, d; and the distance between the observing eye and the halo-active ice crystals, d c , is almost linear.

Fig. 6
Fig. 6

When the alum-crystal-covered plate is inclined, the three halos are perceived as eliptical. The plate was inclined toward the light source and formed an angle of ∼45° with the horizontal plane. The horizontal distance between the light source and the plate was 10 cm, and that between the plate and the camera was 60 cm.

Fig. 7
Fig. 7

Analogy to Minnaert’s Cigar generated in a cloud of precipitated alum crystals in a wide glass vessel. The distance between the left and right camera positions was ∼4 cm. A weak stereoscopic effect can be seen in the photographs, coupled or single, even if the two photographs were not simultaneously exposed. Even if a stereo camera had been used, the two objective lenses would not have seen the same crystals over the small distances given.

Fig. 8
Fig. 8

Minnaert’s cigars drawn by computer for (a) 22°, (b) 18.3°, and (c) 9.5° halos. The cigars have been cut to strengthen their three-dimensional forms.

Fig. 9
Fig. 9

Examples of planes intersecting Minnaert’s Cigar at various angles and positions. Left, the cigar of the 22° halo and the intersecting planes, and the equations for the planes. Middle, the form of the intersections. Right, perspective views of the halos corresponding to how they would be perceived by the observer. At the top, the intersections of the two planes are of identical shape. At the middle, the intersection of the right oblique plane is not drawn. Its shape is a mirror image of the intersection drawn.

Tables (1)

Tables Icon

Table 1 Ratio of Short and Long Axes of Minnaert’s Cigar for Halos Descibed in This Paper

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

tan rd=d1-d tanrmax-rd.
d=rdrmax±0.04rmax2.
dc=1-dcos rd.
q=tanrmax/2,
x2+y+cos rmax2=14 sin2 rmax.

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