Optical Effects
Rainbow I
Rainbow II
Rainbow III
Polarisation Rainbow
Halo I
Halo II
Sun Pillar
Sun through clouds
Crepuscular Rays


Rainbow - Series I

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, 1637).

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.