Abstract

In various everyday situations, a characteristic interference pattern can be observed on water surfaces. This pattern can be divided into two overlapping components: a corona and a system of Quételet’s rings, often with only a section of these visible in the form of fringes. We attribute this phenomenon to thin films of small spheres located just above the reflecting water surface. Due to differences in the optical arrangement, explanatory models applicable for conventionally produced Quételet’s rings are not transferable. We present a compatible mathematical model and some obvious analogies in order to explain the occurrence and properties of this phenomenon.

© 2009 Optical Society of America

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References

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  1. H. J. Schlichting, “Farbkränze auf staubigen Gewässern,” Phys. Unserer Zeit 35, 86-89 (2004).
    [CrossRef]
  2. Isaac Newton, Opticks, new ed. (Prometheus,2003). (originally published 1704)
  3. K. Exner, “Ueber die Fraunhofer'schen Ringe, die Quetelet'schen Streifen und verwandte Erscheinungen,” Ann. Phys. (Leipzig) 240, 525-550 (1878).
    [CrossRef]
  4. W. Suhr and H. J. Schlichting, “Coloured rings produced on transparent plates,” Phys. Educ. 42, 566-571 (2007).
    [CrossRef]
  5. G. G. Stokes, “On the colours of thick plates,” Trans. Cambridge Philos. Soc. 9, 147-176 (1856).
  6. A. J. de Witte, “Interference in scattered light,” Am. J. Phys. 35, 301-313 (1967).
    [CrossRef]
  7. V. J. Schaefer “Observations of an early morning cup of coffee,” Am. Sci. 59, 534-535 (1971).
  8. M. Riikonen, “Optical phenomena from algal films on the water surface,” Master's thesis (University of Helsinki, 2008).
  9. Y. S. Kaganovskii, V. D. Freilikher, E. Kanzieper, Y. Nafcha, M. Rosenbluh, and I. M. Fuks, “Light scattering from slightly rough dielectric films,” J. Opt. Soc. Am. A 16, 331-338 (1999).
    [CrossRef]
  10. S. Lecler, Y. Takakura, and P. Meyrueis, “Interpretation of light scattering by a bisphere in the electrodynamic regime based on apertures interference and cavity resonance,” J. Opt. A: Pure Appl. Opt. 9, 802-810 (2007).
    [CrossRef]
  11. P. Laven, “Simulation of rainbows, coronas and glories by use of Mie theory,” Appl. Opt. 42, 436-444 (2003).
    [CrossRef] [PubMed]
  12. M. I. Mishchenko, D. W. Mackowski, and L. D. Travis, “Scattering of light by bispheres with touching and separated components,” Appl. Opt. 34, 4589-4599 (1995).
    [CrossRef] [PubMed]

2007 (2)

W. Suhr and H. J. Schlichting, “Coloured rings produced on transparent plates,” Phys. Educ. 42, 566-571 (2007).
[CrossRef]

S. Lecler, Y. Takakura, and P. Meyrueis, “Interpretation of light scattering by a bisphere in the electrodynamic regime based on apertures interference and cavity resonance,” J. Opt. A: Pure Appl. Opt. 9, 802-810 (2007).
[CrossRef]

2004 (1)

H. J. Schlichting, “Farbkränze auf staubigen Gewässern,” Phys. Unserer Zeit 35, 86-89 (2004).
[CrossRef]

2003 (1)

1999 (1)

1995 (1)

1971 (1)

V. J. Schaefer “Observations of an early morning cup of coffee,” Am. Sci. 59, 534-535 (1971).

1967 (1)

A. J. de Witte, “Interference in scattered light,” Am. J. Phys. 35, 301-313 (1967).
[CrossRef]

1878 (1)

K. Exner, “Ueber die Fraunhofer'schen Ringe, die Quetelet'schen Streifen und verwandte Erscheinungen,” Ann. Phys. (Leipzig) 240, 525-550 (1878).
[CrossRef]

1856 (1)

G. G. Stokes, “On the colours of thick plates,” Trans. Cambridge Philos. Soc. 9, 147-176 (1856).

de Witte, A. J.

A. J. de Witte, “Interference in scattered light,” Am. J. Phys. 35, 301-313 (1967).
[CrossRef]

Exner, K.

K. Exner, “Ueber die Fraunhofer'schen Ringe, die Quetelet'schen Streifen und verwandte Erscheinungen,” Ann. Phys. (Leipzig) 240, 525-550 (1878).
[CrossRef]

Freilikher, V. D.

Fuks, I. M.

Kaganovskii, Y. S.

Kanzieper, E.

Laven, P.

Lecler, S.

S. Lecler, Y. Takakura, and P. Meyrueis, “Interpretation of light scattering by a bisphere in the electrodynamic regime based on apertures interference and cavity resonance,” J. Opt. A: Pure Appl. Opt. 9, 802-810 (2007).
[CrossRef]

Mackowski, D. W.

Meyrueis, P.

S. Lecler, Y. Takakura, and P. Meyrueis, “Interpretation of light scattering by a bisphere in the electrodynamic regime based on apertures interference and cavity resonance,” J. Opt. A: Pure Appl. Opt. 9, 802-810 (2007).
[CrossRef]

Mishchenko, M. I.

Nafcha, Y.

Newton, Isaac

Isaac Newton, Opticks, new ed. (Prometheus,2003). (originally published 1704)

Riikonen, M.

M. Riikonen, “Optical phenomena from algal films on the water surface,” Master's thesis (University of Helsinki, 2008).

Rosenbluh, M.

Schaefer, V. J.

V. J. Schaefer “Observations of an early morning cup of coffee,” Am. Sci. 59, 534-535 (1971).

Schlichting, H. J.

W. Suhr and H. J. Schlichting, “Coloured rings produced on transparent plates,” Phys. Educ. 42, 566-571 (2007).
[CrossRef]

H. J. Schlichting, “Farbkränze auf staubigen Gewässern,” Phys. Unserer Zeit 35, 86-89 (2004).
[CrossRef]

Stokes, G. G.

G. G. Stokes, “On the colours of thick plates,” Trans. Cambridge Philos. Soc. 9, 147-176 (1856).

Suhr, W.

W. Suhr and H. J. Schlichting, “Coloured rings produced on transparent plates,” Phys. Educ. 42, 566-571 (2007).
[CrossRef]

Takakura, Y.

S. Lecler, Y. Takakura, and P. Meyrueis, “Interpretation of light scattering by a bisphere in the electrodynamic regime based on apertures interference and cavity resonance,” J. Opt. A: Pure Appl. Opt. 9, 802-810 (2007).
[CrossRef]

Travis, L. D.

Am. J. Phys. (1)

A. J. de Witte, “Interference in scattered light,” Am. J. Phys. 35, 301-313 (1967).
[CrossRef]

Am. Sci. (1)

V. J. Schaefer “Observations of an early morning cup of coffee,” Am. Sci. 59, 534-535 (1971).

Ann. Phys. (Leipzig) (1)

K. Exner, “Ueber die Fraunhofer'schen Ringe, die Quetelet'schen Streifen und verwandte Erscheinungen,” Ann. Phys. (Leipzig) 240, 525-550 (1878).
[CrossRef]

Appl. Opt. (2)

J. Opt. A: Pure Appl. Opt. (1)

S. Lecler, Y. Takakura, and P. Meyrueis, “Interpretation of light scattering by a bisphere in the electrodynamic regime based on apertures interference and cavity resonance,” J. Opt. A: Pure Appl. Opt. 9, 802-810 (2007).
[CrossRef]

J. Opt. Soc. Am. A (1)

Phys. Educ. (1)

W. Suhr and H. J. Schlichting, “Coloured rings produced on transparent plates,” Phys. Educ. 42, 566-571 (2007).
[CrossRef]

Phys. Unserer Zeit (1)

H. J. Schlichting, “Farbkränze auf staubigen Gewässern,” Phys. Unserer Zeit 35, 86-89 (2004).
[CrossRef]

Trans. Cambridge Philos. Soc. (1)

G. G. Stokes, “On the colours of thick plates,” Trans. Cambridge Philos. Soc. 9, 147-176 (1856).

Other (2)

Isaac Newton, Opticks, new ed. (Prometheus,2003). (originally published 1704)

M. Riikonen, “Optical phenomena from algal films on the water surface,” Master's thesis (University of Helsinki, 2008).

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Figures (13)

Fig. 1
Fig. 1

Algal film on the surface of the water causes the interference pattern surrounding the reflection of the Sun.

Fig. 2
Fig. 2

View from a short distance of an interference pattern caused by an algal film on a sample of water from the pond shown in Fig. 1. Slightly bent Quételet’s fringes overlap a corona that surrounds the reflection of the artificial light source.

Fig. 3
Fig. 3

Close-up image of a thin layer of water droplets that are levitated by the flux of water vapor from the surface of hot water ( 70 ° C ).

Fig. 4
Fig. 4

Top: focusing on the layer of droplets on the water surface makes the corona appear blurry. Bottom: if, instead, the focus is shifted to the image of the light source, a more pronounced corona as well as, horizontal fringes emerge.

Fig. 5
Fig. 5

This interference pattern was projected in the direction of regular reflection with a 60 μm diameter glass bead on a surface-coated mirror illuminated by the beam of a green laser. The pattern consists of a system of rings superimposed with horizontal fringes.

Fig. 6
Fig. 6

Schematic sectional view of a small sphere on a specular surface. The incident rays I 1 and I 2 are scattered at C.

Fig. 7
Fig. 7

Assumed path of rays in Fig. 6, complemented by the mirror world. This figure offers a clear diagram for computation of the path difference δ.

Fig. 8
Fig. 8

Analogous model of the optical constellation shown in Fig. 7, consisting of two 60 μm diameter glass beads on a glass slide.

Fig. 9
Fig. 9

Interference pattern projected forward to a screen, with the bisphere shown in Fig. 8 illuminated by a green laser beam.

Fig. 10
Fig. 10

Direct view of an interference pattern on a surface-coated mirror covered with lycopodium spores and illuminated with white light.

Fig. 11
Fig. 11

Ensemble of 60 μm diameter glass beads on a surface-coated mirror illuminated with white light. A corona overlapped by Quételet’s fringes occurs around the reflection of the source of the light. (Inset: using a shorter shutter speed improved the visibility of the corona.) Both of these phenomena exhibit only the first four orders of interference.

Fig. 12
Fig. 12

Comparison between the result of a laboratory experiment and a corresponding simulation. Right: the interference pattern was projected in the forward direction with hot water illuminated by the beam of a green laser. Left: the respective interference pattern for an ensemble of disperse spheres r ¯ = 8 μm ( ± 5 % ) as calculated with our model. To obtain adequate spacing of Quételet’s fringes, we also had to assume that the droplets hover 3 μm above the water.

Fig. 13
Fig. 13

Superposition of a glory with Quételet’s fringes. The interference pattern is a result of backscattering by a single 60 μm diameter glass bead on a surface-coated mirror illuminated by a green laser beam.

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