Abstract

Old and new laboratory experiments on atmospheric optics with a focus on mirages, rainbows, and halos are presented. Some qualitative demonstrations serve primarily didactical purposes, e.g., by proving the existence of curved light rays in media with a gradient of the index of refraction, by directly visualizing the minimum-deviation curve for rainbow paths in water droplets, or by helping to elucidate the ray classes in hexagons that contribute to a specific halo. In addition, quantitative experiments allow a direct comparison of angular positions and intensities with analytical computations or Monte Carlo simulations of light scattering from small water droplets or ice hexagons. In particular, the latter can help us to understand complex halo phenomena.

© 1998 Optical Society of America

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References

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  1. M. G. J. Minnaert, Light and Color in the Outdoors (Springer, Berlin, 1993); English edition entitled The Nature of Light and Colour in the Open Air (Dover, New York, 1954).
  2. R. Greenler, Rainbows, Halos and Glories (Cambridge U. Press, Cambridge, 1980).
  3. W. Tape, Atmospheric Halos (American Geophysical Society, Washington, D.C., 1994).
    [CrossRef]
  4. D. K. Lynch, W. Livingston, Color and Light in Nature (Cambridge U. Press, Cambridge, 1995).
  5. Feature issue on light and color, J. Opt. Soc. Am. A 4, (1987); Appl. Opt. 30,(24) (1991); Appl. Opt. 33,(21) (1994).
  6. J. Müller, Atlas zum Lehrbuch der Kosmischen Physik (Vieweg, Braunschweig, 1856).
  7. R. Greenler, “Laboratory simulation of inferior and superior mirages,” J. Opt. Soc. Am. A 4, 589–590 (1987).
    [CrossRef]
  8. R. W. Pohl, Einführung in die Physik: Optik und Atomphysik, 9th ed. (Springer, Berlin, 1954).
  9. W. A. Strouse, “Bouncing light beam,” Am. J. Phys. 40, 913–914 (1972).
    [CrossRef]
  10. R. W. Wood, “Some experiments on artificial mirages and tornadoes,” Philos. Mag. 47, 349–353 (1899).
  11. Fata Morganen—Zauberspiegel am Horizont, television film produced by M. Engler, First Broadcast 8 March 1996 by ARTE.
  12. C. Tape, “Mirages,” presented at the conference on Light and Color in the Open Air, Santa Fe, New Mexico, February 1997.
  13. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
  14. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  15. U. Kreibig, M. Vollmer, Optical Properties of Metal Clusters, Vol. 25 of the Springer Series on Material Sciences (Springer-Verlag, New York, 1995).
    [CrossRef]
  16. C. F. Boyer, The Rainbow: From Myth to Mathematics (Princeton U. Press, Princeton, N.J., 1987).
  17. Oeuvres de Descartes, Charles Adam, Paul Tannery, eds., Discours de la Méthode et Essais VI: Les Meteors–Discours VIII de l’Arc en Ciel (1637) (Vrin, Paris, 1982).
  18. I. Newton, Opticks: or a Treatise of the Reflexions, Refractions, Inflexions and Colours (Royal Society, London, 1704);Opticks: or a Treatise of the Reflexions, Refractions, Inflexions and Colours (German ed. Vieweg, Braunschweig, 1983).
  19. H. M. Nussenzveig, “The theory of the rainbow,” Sci. Am. 237, 116–127 (1977);“Complex angular momentum theory of the rainbow and the glory,” J. Opt. Soc. Am. 69, 1068–1079 (1979).
    [CrossRef]
  20. J. M. Pernter, F. M. Exner, Meteorologische Optik, 2nd ed. (Braumüller, Vienna, 1922).
  21. J. Walker, “Multiple rainbows from single drops of water and other liquids,” Am. J. Phys. 44, 421–433 (1976); “How to create and observe a dozen rainbows in a single drop of water,” Sci. Am. 237, 138–144 (1977); “Mysteries of rainbows, notably their rare supernumerary arcs,” Sci. Am. 240, 146–152 (1980).
  22. K. Sassen, “Angular scattering and rainbow formation in pendant drops,” J. Opt. Soc. Am. 69, 1083–1089 (1979).
    [CrossRef]
  23. A. B. Fraser, “Why can the supernumerary bows be seen in a rain shower?,” J. Opt. Soc. Am. 73, 1626–1628 (1983).
    [CrossRef]
  24. E. Tränkle, R. G. Greenler, “Multiple-scattering effects in halo phenomena,” J. Opt. Soc. Am. A 4, 591–599 (1987).
    [CrossRef]
  25. K. Sassen, Department of Meteorology, University of Utah, Salt Lake City, Utah 84112 (personal communication, February1997).
  26. G. P. Können, J. Tinbergen, Polarized Light in Nature (Cambridge U. Press, Cambridge, 1985); “Polarization structures in parhelic circles and in 120° parhelia,” Appl. Opt. 37, 1457–1464 (1998).
  27. L. Bergmann, C. Schäfer, Lehrbuch der Experimentalphysik III: Optik, 7th ed. (de Gruyter, Berlin, 1978).
  28. R. Greenler, Department of Physics, University of Wisconsin-Milwaukee, Milwaukee, Wis. 53201 (personal communication, February1997).

1987

1983

1979

1977

H. M. Nussenzveig, “The theory of the rainbow,” Sci. Am. 237, 116–127 (1977);“Complex angular momentum theory of the rainbow and the glory,” J. Opt. Soc. Am. 69, 1068–1079 (1979).
[CrossRef]

1976

J. Walker, “Multiple rainbows from single drops of water and other liquids,” Am. J. Phys. 44, 421–433 (1976); “How to create and observe a dozen rainbows in a single drop of water,” Sci. Am. 237, 138–144 (1977); “Mysteries of rainbows, notably their rare supernumerary arcs,” Sci. Am. 240, 146–152 (1980).

1972

W. A. Strouse, “Bouncing light beam,” Am. J. Phys. 40, 913–914 (1972).
[CrossRef]

1899

R. W. Wood, “Some experiments on artificial mirages and tornadoes,” Philos. Mag. 47, 349–353 (1899).

Bergmann, L.

L. Bergmann, C. Schäfer, Lehrbuch der Experimentalphysik III: Optik, 7th ed. (de Gruyter, Berlin, 1978).

Bohren, C. F.

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

Boyer, C. F.

C. F. Boyer, The Rainbow: From Myth to Mathematics (Princeton U. Press, Princeton, N.J., 1987).

Exner, F. M.

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

Fraser, A. B.

Greenler, R.

R. Greenler, “Laboratory simulation of inferior and superior mirages,” J. Opt. Soc. Am. A 4, 589–590 (1987).
[CrossRef]

R. Greenler, Department of Physics, University of Wisconsin-Milwaukee, Milwaukee, Wis. 53201 (personal communication, February1997).

R. Greenler, Rainbows, Halos and Glories (Cambridge U. Press, Cambridge, 1980).

Greenler, R. G.

Huffman, D. R.

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

Können, G. P.

G. P. Können, J. Tinbergen, Polarized Light in Nature (Cambridge U. Press, Cambridge, 1985); “Polarization structures in parhelic circles and in 120° parhelia,” Appl. Opt. 37, 1457–1464 (1998).

Kreibig, U.

U. Kreibig, M. Vollmer, Optical Properties of Metal Clusters, Vol. 25 of the Springer Series on Material Sciences (Springer-Verlag, New York, 1995).
[CrossRef]

Livingston, W.

D. K. Lynch, W. Livingston, Color and Light in Nature (Cambridge U. Press, Cambridge, 1995).

Lynch, D. K.

D. K. Lynch, W. Livingston, Color and Light in Nature (Cambridge U. Press, Cambridge, 1995).

Minnaert, M. G. J.

M. G. J. Minnaert, Light and Color in the Outdoors (Springer, Berlin, 1993); English edition entitled The Nature of Light and Colour in the Open Air (Dover, New York, 1954).

Müller, J.

J. Müller, Atlas zum Lehrbuch der Kosmischen Physik (Vieweg, Braunschweig, 1856).

Newton, I.

I. Newton, Opticks: or a Treatise of the Reflexions, Refractions, Inflexions and Colours (Royal Society, London, 1704);Opticks: or a Treatise of the Reflexions, Refractions, Inflexions and Colours (German ed. Vieweg, Braunschweig, 1983).

Nussenzveig, H. M.

H. M. Nussenzveig, “The theory of the rainbow,” Sci. Am. 237, 116–127 (1977);“Complex angular momentum theory of the rainbow and the glory,” J. Opt. Soc. Am. 69, 1068–1079 (1979).
[CrossRef]

Pernter, J. M.

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

Pohl, R. W.

R. W. Pohl, Einführung in die Physik: Optik und Atomphysik, 9th ed. (Springer, Berlin, 1954).

Sassen, K.

K. Sassen, “Angular scattering and rainbow formation in pendant drops,” J. Opt. Soc. Am. 69, 1083–1089 (1979).
[CrossRef]

K. Sassen, Department of Meteorology, University of Utah, Salt Lake City, Utah 84112 (personal communication, February1997).

Schäfer, C.

L. Bergmann, C. Schäfer, Lehrbuch der Experimentalphysik III: Optik, 7th ed. (de Gruyter, Berlin, 1978).

Strouse, W. A.

W. A. Strouse, “Bouncing light beam,” Am. J. Phys. 40, 913–914 (1972).
[CrossRef]

Tape, C.

C. Tape, “Mirages,” presented at the conference on Light and Color in the Open Air, Santa Fe, New Mexico, February 1997.

Tape, W.

W. Tape, Atmospheric Halos (American Geophysical Society, Washington, D.C., 1994).
[CrossRef]

Tinbergen, J.

G. P. Können, J. Tinbergen, Polarized Light in Nature (Cambridge U. Press, Cambridge, 1985); “Polarization structures in parhelic circles and in 120° parhelia,” Appl. Opt. 37, 1457–1464 (1998).

Tränkle, E.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

Vollmer, M.

U. Kreibig, M. Vollmer, Optical Properties of Metal Clusters, Vol. 25 of the Springer Series on Material Sciences (Springer-Verlag, New York, 1995).
[CrossRef]

Walker, J.

J. Walker, “Multiple rainbows from single drops of water and other liquids,” Am. J. Phys. 44, 421–433 (1976); “How to create and observe a dozen rainbows in a single drop of water,” Sci. Am. 237, 138–144 (1977); “Mysteries of rainbows, notably their rare supernumerary arcs,” Sci. Am. 240, 146–152 (1980).

Wood, R. W.

R. W. Wood, “Some experiments on artificial mirages and tornadoes,” Philos. Mag. 47, 349–353 (1899).

Am. J. Phys.

W. A. Strouse, “Bouncing light beam,” Am. J. Phys. 40, 913–914 (1972).
[CrossRef]

J. Walker, “Multiple rainbows from single drops of water and other liquids,” Am. J. Phys. 44, 421–433 (1976); “How to create and observe a dozen rainbows in a single drop of water,” Sci. Am. 237, 138–144 (1977); “Mysteries of rainbows, notably their rare supernumerary arcs,” Sci. Am. 240, 146–152 (1980).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Philos. Mag.

R. W. Wood, “Some experiments on artificial mirages and tornadoes,” Philos. Mag. 47, 349–353 (1899).

Sci. Am.

H. M. Nussenzveig, “The theory of the rainbow,” Sci. Am. 237, 116–127 (1977);“Complex angular momentum theory of the rainbow and the glory,” J. Opt. Soc. Am. 69, 1068–1079 (1979).
[CrossRef]

Other

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

R. W. Pohl, Einführung in die Physik: Optik und Atomphysik, 9th ed. (Springer, Berlin, 1954).

Fata Morganen—Zauberspiegel am Horizont, television film produced by M. Engler, First Broadcast 8 March 1996 by ARTE.

C. Tape, “Mirages,” presented at the conference on Light and Color in the Open Air, Santa Fe, New Mexico, February 1997.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

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

U. Kreibig, M. Vollmer, Optical Properties of Metal Clusters, Vol. 25 of the Springer Series on Material Sciences (Springer-Verlag, New York, 1995).
[CrossRef]

C. F. Boyer, The Rainbow: From Myth to Mathematics (Princeton U. Press, Princeton, N.J., 1987).

Oeuvres de Descartes, Charles Adam, Paul Tannery, eds., Discours de la Méthode et Essais VI: Les Meteors–Discours VIII de l’Arc en Ciel (1637) (Vrin, Paris, 1982).

I. Newton, Opticks: or a Treatise of the Reflexions, Refractions, Inflexions and Colours (Royal Society, London, 1704);Opticks: or a Treatise of the Reflexions, Refractions, Inflexions and Colours (German ed. Vieweg, Braunschweig, 1983).

J. Müller, Atlas zum Lehrbuch der Kosmischen Physik (Vieweg, Braunschweig, 1856).

K. Sassen, Department of Meteorology, University of Utah, Salt Lake City, Utah 84112 (personal communication, February1997).

G. P. Können, J. Tinbergen, Polarized Light in Nature (Cambridge U. Press, Cambridge, 1985); “Polarization structures in parhelic circles and in 120° parhelia,” Appl. Opt. 37, 1457–1464 (1998).

L. Bergmann, C. Schäfer, Lehrbuch der Experimentalphysik III: Optik, 7th ed. (de Gruyter, Berlin, 1978).

R. Greenler, Department of Physics, University of Wisconsin-Milwaukee, Milwaukee, Wis. 53201 (personal communication, February1997).

M. G. J. Minnaert, Light and Color in the Outdoors (Springer, Berlin, 1993); English edition entitled The Nature of Light and Colour in the Open Air (Dover, New York, 1954).

R. Greenler, Rainbows, Halos and Glories (Cambridge U. Press, Cambridge, 1980).

W. Tape, Atmospheric Halos (American Geophysical Society, Washington, D.C., 1994).
[CrossRef]

D. K. Lynch, W. Livingston, Color and Light in Nature (Cambridge U. Press, Cambridge, 1995).

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Figures (16)

Fig. 1
Fig. 1

Mirage in the desert (from Ref. 6).

Fig. 2
Fig. 2

Curved He–Ne laser beam in a tank with fresh water on top of saturated salt water, i.e., an artificial inversion layer.

Fig. 3
Fig. 3

Object, like the ace of hearts, (a) observed over a hot metal plate (length 3 m) gives rise to (b) an inferior mirage. Total distance from object to observer ≈6 m, focal length 210 mm.

Fig. 4
Fig. 4

Objects (two colored tops and the words FATA MORGANA) as viewed through (a) plain water, (b) the artificial inversion layer. The three-part mirage in (b) corresponds to a superior mirage.

Fig. 5
Fig. 5

Snapshots of a videosequence of transient effects in mirages due to wavelike disturbences. Some parts of the mirages vanish and reappear periodically.

Fig. 6
Fig. 6

Rainbow caustics of a single water droplet, illuminated by white light from an arc lamp.

Fig. 7
Fig. 7

Experimentally observed rainbow light paths of higher-order rainbows within (a) the water drop, (b) the theoretical ray paths (after Ref. 20).

Fig. 8
Fig. 8

Airy ring systems of primary bow due to illumination with two colinear red and green He–Ne lasers.

Fig. 9
Fig. 9

Airy ring systems of first-, second-, fifth-, and sixth-order rainbows for a red He–Ne laser.

Fig. 10
Fig. 10

Change of measured intensity of the first Airy ring maximum of the primary bow as a function of time. (a) The intensity decreases because of the decrease of the drop size, (b) Airy ring systems for a primary bow for a spherical water drop of R ≈ 1 mm and λ = 632.8 nm. The intensities as functions of time were corrected according to (a).

Fig. 11
Fig. 11

Airy rings (λ = 632.8 nm) of primary and secondary bows for a cylinder of flowing water (2R = 0.465 mm).

Fig. 12
Fig. 12

Artificial parhelia and the parhelic circle as observed with a glass prism (n = 1.62) for a Sun elevation of (a) 0°, (b) ≈ 20°.

Fig. 13
Fig. 13

(a) Intensities of parhelia and parhelic circles for a glass prism (n = 1.62) illuminated by a He–Ne laser (λ = 633 nm) as functions of the deviation angle, (b) Monte Carlo simulation of the experiment (courtesy E. Tränkle).

Fig. 14
Fig. 14

Intensities of parhelia and parhelic circles for a glass hexagon (n = 1.48) illuminated by a He–Ne laser (λ = 633 nm) as functions of the deviation angle.

Fig. 15
Fig. 15

Theoretical ray path responsible for the 90° parhelia.

Fig. 16
Fig. 16

Halo display due to hexagons (n = 1.48), rotating in Parry arc orientation and illuminated with white light from a slide projector. Sun elevations of (a) 0°, (b) ≈40° were chosen. The halos were projected on a hemisphere of 1-m diameter.

Equations (3)

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cos N α inc = n 2 - 1 N + 1 2 - 1 1 / 2 .
δ α inc = 2 α inc + N + 1 π - 2 α refr - π ,
γ min = 2   arcsin n   sin γ 2 - γ .

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