Photographic evidence for the third-order rainbow

Michael Großmann; Elmar Schmidt; Alexander Haußmann

doi:10.1364/AO.50.00F134

Applied Optics
Vol. 50,
Issue 28,
pp. F134-F141
(2011)
•https://doi.org/10.1364/AO.50.00F134

Photographic evidence for the third-order rainbow

Michael Großmann, Elmar Schmidt, and Alexander Haußmann

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Michael Großmann, Elmar Schmidt, and Alexander Haußmann, "Photographic evidence for the third-order rainbow," Appl. Opt. 50, F134-F141 (2011)

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Abstract

The first likely photographic observation of the tertiary rainbow caused by sunlight in the open air is reported and analyzed. Whereas primary and secondary rainbows are rather common and easily seen phenomena in atmospheric optics, the tertiary rainbow appears in the sunward side of the sky and is thus largely masked by forward scattered light. Up to now, only a few visual reports and no reliable photographs of the tertiary rainbow are known. Evidence of a third-order rainbow has been obtained by using image processing techniques on a digital photograph that contains no obvious indication of such a rainbow. To rule out any misinterpretation of artifacts, we carefully calibrated the image in order to compare the observed bow’s angular position and dispersion with those predicted by theory.

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x [pixel]	y [pixel]	Elevation $[°]$	Azimuth $[°]$	Angular Distance from Sun $[°]$
17.5	121	37.3	256.5	41.8
10.5	109	35.6	255.1	41.8
4.5	99	34.1	253.8	41.9
$- 0.5$	88	32.5	252.8	41.9
$- 4.5$	75	30.6	251.9	41.8
$- 9.5$	65	29.0	251.0	41.9
$- 12.5$	53	27.1	250.3	41.7
$- 15.5$	42	25.4	249.8	41.7
$- 18.5$	31	23.7	249.2	41.7
$- 21.5$	21	22.1	248.6	41.8
$- 23.5$	10	20.4	248.2	41.8
$- 25.5$	$- 3$	18.3	247.9	41.8
$- 26.5$	$- 14$	16.6	247.7	41.8
$- 26.5$	$- 24$	15.0	247.6	41.7
$- 27.5$	$- 35$	13.3	247.4	41.8

Sensor Channel	Peak Wavelength	Centroid Wavelength	Effect of Including Reddened Sunlight	Choice for Fitting the Rainbow Data	Refractive Index Water-Air	Descartes Angle (Tertiary Rainbow)
Red	$592 nm$	$587 nm$	$+ 8 nm$	$600 nm$	1.3337	$41.49 °$
Green	$525 nm$	$531 nm$	$+ 4 nm$	$530 nm$	1.3361	$40.59 °$
Blue	$452 nm$	$476 nm$	$+ 6 nm$	$460 nm$	1.3396	$39.31 °$

x [pixel]	y [pixel]	Elevation $[°]$	Azimuth $[°]$	Angular Distance from Sun $[°]$
17.5	121	37.3	256.5	41.8
10.5	109	35.6	255.1	41.8
4.5	99	34.1	253.8	41.9
$- 0.5$	88	32.5	252.8	41.9
$- 4.5$	75	30.6	251.9	41.8
$- 9.5$	65	29.0	251.0	41.9
$- 12.5$	53	27.1	250.3	41.7
$- 15.5$	42	25.4	249.8	41.7
$- 18.5$	31	23.7	249.2	41.7
$- 21.5$	21	22.1	248.6	41.8
$- 23.5$	10	20.4	248.2	41.8
$- 25.5$	$- 3$	18.3	247.9	41.8
$- 26.5$	$- 14$	16.6	247.7	41.8
$- 26.5$	$- 24$	15.0	247.6	41.7
$- 27.5$	$- 35$	13.3	247.4	41.8

Sensor Channel	Peak Wavelength	Centroid Wavelength	Effect of Including Reddened Sunlight	Choice for Fitting the Rainbow Data	Refractive Index Water-Air	Descartes Angle (Tertiary Rainbow)
Red	$592 nm$	$587 nm$	$+ 8 nm$	$600 nm$	1.3337	$41.49 °$
Green	$525 nm$	$531 nm$	$+ 4 nm$	$530 nm$	1.3361	$40.59 °$
Blue	$452 nm$	$476 nm$	$+ 6 nm$	$460 nm$	1.3396	$39.31 °$

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