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.

©1999 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Laboratory experiments in atmospheric optics

Michael Vollmer and Robert Tammer
Appl. Opt. 37(9) 1557-1568 (1998)

Rainbows, water droplets, and seeing—slow motion analysis of experiments in atmospheric optics

Michael Vollmer and Klaus-Peter Möllmann
Appl. Opt. 50(28) F21-F28 (2011)

Atmospheric optics in the near infrared

Michael Vollmer and Joseph A. Shaw
Appl. Opt. 56(19) G145-G155 (2017)

More Recommended Articles

References

  • View by:
  • Article Order
  • |
  • Year
  • |
  • Author
  • |
  • Publication
  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 and W. Livingston, Color and Light in Nature (Cambridge U. Press, Cambridge, 1995).
  5. Feature issue on light and color, J. Opt. Soc. Am. A4, (1987); Appl. Opt.30,(24) (1991); Appl. Opt.33,(21) (1994).
    [PubMed]
  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 undAtomphysik, 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 and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  15. U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters, Vol. 25 of the Springer Series on Material Sciences (Springer-Verlag, New York, 1995).
  16. C. F. Boyer, The Rainbow: From Myth to Mathematics (Princeton U. Press, Princeton, N.J., 1987).
  17. Oeuvres de Descartes, Charles Adam and Paul Tannery, eds., Discours de la Méthode et Essais VI: Les Meteors-Discours VIII de lArc en Ciel (1637) (Vrin, Paris, 1982).
  18. I. Newton, Opticks: or a Treatise of the Reflexions, Refractions, Inflexions and Colours (Royal Society, London, 1704); (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 and 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).
    [Crossref]
  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 and 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, February 1997).
  26. G. P. Können and 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).
    [Crossref]
  27. L. Bergmann and C. Schäfer, Lehrbuch der Experimental-physik III: Optik, 7th ed. (de Gruyter, Berlin, 1978).
  28. R. Greenler, Department of Physics, University of Wisconsin-Milwaukee, Milwaukee, Wis. 53201 (personal communication, February 1997).

1987 (2)

1983 (1)

1979 (1)

1972 (1)

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

1899 (1)

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

Bergmann, L.

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

Bohren, C. F.

C. F. Bohren and 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 and 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, February 1997).

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

Greenler, R. G.

Huffman, D. R.

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

Können, G. P.

G. P. Können and 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).
[Crossref]

Kreibig, U.

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

Livingston, W.

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

Lynch, D. K.

D. K. Lynch and 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); (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 and F. M. Exner, Meteorologische Optik, 2nd ed. (Braumüller, Vienna, 1922).

Pohl, R. W.

R. W. Pohl, Einführung in die Physik: Optik undAtomphysik, 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, February 1997).

Schäfer, C.

L. Bergmann and C. Schäfer, Lehrbuch der Experimental-physik 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 and 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).
[Crossref]

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

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).
[Crossref]

Wood, R. W.

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

Am. J. Phys. (1)

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

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (2)

Philos. Mag. (1)

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

Other (22)

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

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

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

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

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

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]

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

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).
[Crossref]

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

Feature issue on light and color, J. Opt. Soc. Am. A4, (1987); Appl. Opt.30,(24) (1991); Appl. Opt.33,(21) (1994).
[PubMed]

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, February 1997).

G. P. Können and 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).
[Crossref]

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

R. Greenler, Department of Physics, University of Wisconsin-Milwaukee, Milwaukee, Wis. 53201 (personal communication, February 1997).

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

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (16)

Fig. 1.
Fig. 1. Mirage in the desert (from Ref. 6).

Download Full Size | PPT Slide | PDF

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.

Download Full Size | PPT Slide | PDF

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.

Download Full Size | PPT Slide | PDF

Fig. 4.
Fig. 4. Objects (two colored tops and the words FATA MOR-GANA) as viewed through (a) plain water, (b) the artificial inversion layer. The three-part mirage in (b) corresponds to a superior mirage.

Download Full Size | PPT Slide | PDF

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.

Download Full Size | PPT Slide | PDF

Fig. 6.
Fig. 6. Rainbow caustics of a single water droplet, illuminated by white light from an arc lamp.

Download Full Size | PPT Slide | PDF

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).

Download Full Size | PPT Slide | PDF

Fig. 8.
Fig. 8. Airy ring systems of primary bow due to illumination with two colinear red and green He-Ne lasers.

Download Full Size | PPT Slide | PDF

Fig. 9.
Fig. 9. Airy ring systems of first-, second-, fifth-, and sixth-order rainbows for a red He-Ne laser.

Download Full Size | PPT Slide | PDF

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).

Download Full Size | PPT Slide | PDF

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).

Download Full Size | PPT Slide | PDF

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°.

Download Full Size | PPT Slide | PDF

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).

Download Full Size | PPT Slide | PDF

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.

Download Full Size | PPT Slide | PDF

Fig. 15.
Fig. 15. Theoretical ray path responsible for the 90° parhelia.

Download Full Size | PPT Slide | PDF

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.

Download Full Size | PPT Slide | PDF

Equations (3)

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

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 .

Metrics