These images were taken from the roof of the new Science building
at the Johannes Gutenberg University in Mainz. Especially in Rainbow3.jpg
the colour separation can be well noticed. Rainbow1.jpg presents
the primary arc at an angle of 42 degrees around the opposite
point of the sun as well as the secondary rainbow at an angle
of 52 degrees.
The deeper the sun the larger is the size of the rainbow, since
the opposite point of the sun (that means the extension of the
line sun-observer to the reproducing cloud band) is higher. The
geographic latitude is also important. Even under the condition
of a favourable position of the rainy cloud around noon time an
observer at the latitude of 50 degrees will not see a rainbow,
since the opposite point of the sun is below the horizon. The
angles where primary and secondary rainbows appear are always
the same due to the processes of geometrical optics, necessary
to generate a rainbow.
The colour separation is caused by different refraction indices
of water at different wavelengths of the light (for red light
1.329, for blue light 1.333). Therefore blue light is refracted
stronger than red light. Entering the water droplet and then leaving
it again in direction to the observer the sunlight is refracted
twice and therefore colour separation is even enhanced (Descartes-Theory,
The red colour is found at the outside of the primary rainbow,
whereas it is the inner ring of the secondary rainbow. Therefore
the red rings of the two bows are always vicinal. Rainbows where
the outer as well as the inner rings are blue (ArcEnCiel.jpg)
only occur in the paintings by Camille Pissaro.
Primary and secondary rainbows are formed together when the droplets
of the cloud almost have the same size, since not only refraction,
but also interference is important. According to Airy-Theory (1836)
light beams having certain time differences after passing the
droplets, can extinguish each other.
According to the calculations of the Airy-Theory there is a relationship
between the approximate droplet size and the colour intensity.
- Intense purple light with strong green and pure red indicate
raindrops with a diameter of 1 to 2 mm.
- Droplet diameters around 0.5 mm generate secondary rainbows,
which are only purple and green and cause only a weak intensity
of the red at the primary bow.
- Small droplets with a diameter between 0.2 and 0.3 mm are responsible
for intense yellow in the secondary rainbow and a "washy"
red in the primary one.
- Fog droplets with a diameter smaller then 0.1 mm generate pure
white rainbows, which are also called "fog bows".
In theory also the moon-light could generate colourful rainbows,
but their intensity is so weak that we only can see white light.
The colour-sensitive uvulas of the retina require higher intensities
than the black-and white-sensitive rods in the human eye.
The space between the bows is generally darker than those within
the primary bow. This can be also noticed in the images. At the
outside of the secondary rainbow it becomes brighter again. Unfortunately,
this cannot be noticed in Rainbow1.jpg and Rainbow2.jpg because
of the inhomogeneous background. Also this is caused by the laws
of geometrical optics.
Rainbow1-3.jpg: Oliver Hartmann, Mainz, Germany, 2001
Camille Pissaro, "La pleine d'Epluches (Arc en ciel)"
or "De regenboog", Oil on Canvas, 53 cm x 81 cm (1877)
Rijksmuseum Kröller-Möller, Otterloo, The Netherlands
RainbowCDF.jpg: Caspar David Friedrich, "Landscape with Rainbow",
Oil on Canvas, 59 cm x 84.5 cm (around 1810, lost since 1945)
Rainbow4-9.jpg: Jens Mehrens, Ober-Olm near Mainz, Germany, 24
June 2004 between 7:30 and 8:17 p.m.
Rainbow10-12.jpg: S. Borrmann, Luquillo, Puerto Rico, RICO-PRACS
Field Campaign, 18 December 2004, 8:18 a.m.