Abstract

A photograph has been obtained of a natural fifth-order (quinary) rainbow. The photograph was acquired on 8 August 2012 with a digital camera and a polarization filter to maximize contrast of the rainbows with the background. The quinary rainbow, together with its first supernumerary, appears in a contrast-enhanced version of the photograph as broad green and blue-violet color bands within Alexander’s dark band between the primary and secondary rainbows. The red band of the quinary rainbow is obscured by the much brighter secondary rainbow. A comparison with a numerical simulation using the Debye series confirms that the color bands of the quinary rainbow appear at the expected location. The numerical simulation produces a good match with the photograph for a droplet radius of 0.46 mm. The green band of the quinary rainbow is even faintly discernible in the unprocessed photograph, suggesting that under exceptional viewing conditions the green band of the quinary rainbow may be observed visually with the aid of a polarization filter.

© 2014 Optical Society of America

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References

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2015 (1)

2011 (3)

2010 (1)

2005 (1)

2003 (1)

1998 (1)

1996 (1)

1987 (2)

K. V. Beard and C. Chuang, “A new model for the equilibrium shape of raindrops,” J. Atmos. Sci. 44, 1509–1524 (1987).
[Crossref]

G. P. Können, “Appearance of supernumeraries of the secondary rainbow in rain showers,” J. Opt. Soc. Am. A 4, 810–816 (1987).
[Crossref]

1983 (1)

A. B. Fraser, “Why can the supernumerary bows be seen in a rain shower?” J. Opt. Soc. Am. A 73, 1626–1628 (1983).
[Crossref]

1975 (1)

A. W. Green, “An approximation for the shapes of large raindrops,” J. Appl. Meteorol. 14, 1578–1583 (1975).
[Crossref]

1908 (1)

P. Debye, “Das electromagnetische Feld um einen Zylinder und die Theorie des Regenbogens,” Phys. Z. 9, 775–778 (1908).

Beard, K. V.

K. V. Beard and C. Chuang, “A new model for the equilibrium shape of raindrops,” J. Atmos. Sci. 44, 1509–1524 (1987).
[Crossref]

Chuang, C.

K. V. Beard and C. Chuang, “A new model for the equilibrium shape of raindrops,” J. Atmos. Sci. 44, 1509–1524 (1987).
[Crossref]

Ciddor, P. E.

Cowley, L.

L. Cowley, [personal communication (2013)].

Debye, P.

P. Debye, “Das electromagnetische Feld um einen Zylinder und die Theorie des Regenbogens,” Phys. Z. 9, 775–778 (1908).

Fraser, A. B.

A. B. Fraser, “Why can the supernumerary bows be seen in a rain shower?” J. Opt. Soc. Am. A 73, 1626–1628 (1983).
[Crossref]

Grandy, W. T.

W. T. Grandy, Scattering of Waves from Large Spheres (Cambridge University, 2001).

Green, A. W.

A. W. Green, “An approximation for the shapes of large raindrops,” J. Appl. Meteorol. 14, 1578–1583 (1975).
[Crossref]

Großmann, M.

Haußmann, A.

Können, G. P.

Laven, P.

Lee, R. L.

Schmidt, E.

Shen, J.

Theusner, M.

Wang, H.

Appl. Opt. (9)

J. Appl. Meteorol. (1)

A. W. Green, “An approximation for the shapes of large raindrops,” J. Appl. Meteorol. 14, 1578–1583 (1975).
[Crossref]

J. Atmos. Sci. (1)

K. V. Beard and C. Chuang, “A new model for the equilibrium shape of raindrops,” J. Atmos. Sci. 44, 1509–1524 (1987).
[Crossref]

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

G. P. Können, “Appearance of supernumeraries of the secondary rainbow in rain showers,” J. Opt. Soc. Am. A 4, 810–816 (1987).
[Crossref]

A. B. Fraser, “Why can the supernumerary bows be seen in a rain shower?” J. Opt. Soc. Am. A 73, 1626–1628 (1983).
[Crossref]

Phys. Z. (1)

P. Debye, “Das electromagnetische Feld um einen Zylinder und die Theorie des Regenbogens,” Phys. Z. 9, 775–778 (1908).

Other (7)

W. T. Grandy, Scattering of Waves from Large Spheres (Cambridge University, 2001).

L. Cowley, “Atmospheric optics,” http://www.atoptics.co.uk .

L. Cowley, [personal communication (2013)].

D. Bruton, “Approximate RGB values for visible wavelengths,” (1996), http://www.physics.sfasu.edu/astro/color/spectra.html .

P. Laven, “MiePlot,” http://www.philiplaven.com/mieplot.htm .

The International Association for the Properties of Water and Steam, “Release on the refractive index of ordinary water substance as a function of wavelength, temperature and pressure,” (1997), http://www.iapws.org .

H. E. Edens, “Observations of the quinary rainbow,” http://www.weatherscapes.com/quinary/ .

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Figures (6)

Fig. 1.
Fig. 1.

(Top) Unprocessed digital photograph of 8 August 2012 at 23:48:23 UTC. (Bottom) Contrast-enhanced image showing the green and blue-violet color bands of the quinary bow inside the secondary bow. The quinary bow is visible from the top of the dark mountain ridge in the foreground to the top of the frame. With scrutiny, the green color band of the quinary bow is discernible in the original photograph as well.

Fig. 2.
Fig. 2.

Contrast-enhanced photograph with superimposed scattering coordinate frame. The six calibration landmarks are indicated by green squares. Thick lines are drawn at 10° intervals of scattering angle θ and clock angle ϕ; thin lines are drawn at 1° intervals. The almost horizontal white line indicates the astronomical horizon at 0° altitude (about 1° above the true horizon). The pixel-averaging window is indicated by the white polygon at left, along with the start of its trajectory in light gray.

Fig. 3.
Fig. 3.

(Top) Debye-series simulation of the observation showing superimposed orders p=0, p=2, p=3, and p=6. (Middle) Averaged scan of the contrast-enhanced photograph showing part of the quinary bow between the primary and secondary bows. (Bottom) The appearance of the Debye-series order p=6 (quinary bow) by itself, superimposed on the p=0 order (external reflection), which appears a constant dark gray within the interval. All orders p in the top and bottom images are normalized to the maximum intensity of the secondary bow (p=3). The order p=2 was simulated for r=0.275mm; all other orders for r=0.460mm (see text for the motivation for these values). All three images are one-dimensional, extended in height for better visibility.

Fig. 4.
Fig. 4.

Relative intensity light curves of the photograph and Debye-series simulation for the red (R), green (G), and blue (B) color channels. Dotted lines are the Debye-series orders p=0, p=2, and p=3; dashed lines represent order p=6 (quinary bow). Thin solid lines are the summed intensities of orders p=0, p=2, p=3, and p=6. Thick solid lines are the color intensities measured from the averaged photograph, after a linear transformation to correct for an overall gradient in background brightness (see text). The order p=2 was simulated at r=0.275mm and the other orders at r=0.460mm.

Fig. 5.
Fig. 5.

Overlay of contrast-enhanced photograph and Debye-series simulation showing the primary, secondary, and quinary bows. The primary bow was simulated for r=0.275mm and the secondary and quinary bows for r=0.460mm. The overlay was created digitally by applying masking layers to a multilayer image, without manual adjustments in position. A background hue was applied to the Debye-simulation image to assimilate that of the photograph to the left of the primary bow. The color bands of the quinary bow in the photograph match those of the simulated bow in visual appearance.

Fig. 6.
Fig. 6.

While perusing the author’s digital photo archive of 2008–2013, nine additional appearances of the quinary rainbow were identified (Table 4). This contrast-enhanced photograph was obtained at Langmuir Laboratory on 4 September 2009 at 00:48 UTC, at a solar elevation of 8°. The green color band of the quinary bow is visible extending upward from the top of the dark mountain ridge in the foreground to the top of the frame. It is discernible in the unprocessed photograph as well. The photograph was taken with a Nikon D700 camera fitted with a lens at 55 mm focal length and a polarization filter.

Tables (4)

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Table 1. Camera Calibration Parameters

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Table 2. Droplet Radii r Inferred from Measured Angular Separation Δθ between Supernumeraries and Main Maxima, and from Scattering Angles θmax at Peak Intensities

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Table 3. Scattering Angles at Peak Intensities from Photograph (θPhoto) and Simulations (θDebye) for r=0.46mm

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Table 4. Photographic Observations of the Quinary Rainbow to Datea

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