Rainbow

The rainbow is probably the best-known atmospheric phenomenon. Everyone has seen it at least once, though usually by chance. If you want to specifically look for a rainbow, you must know the conditions under which a rainbow appears and where in the sky it can be found. The rainbow is part of a circular arc with a radius of 42° around the antisolar point. It is red on the outside. This is followed by orange, yellow, green, blue, and violet with gradual transitions. A rainbow is only visible when the sun shines while it is raining. Additionally, the sun's altitude must also be less than 42°. If the sun is higher, the antisolar point is more than 42° below the horizon, so the rainbow does not arch above the horizon. In our region, the sun rises up to 60° high in summer. Therefore, one will never see a rainbow around midday in summer. The best viewing conditions are in the evening and morning hours, when the rainbow stands particularly high above the horizon. During the winter months, the sun never rises higher than 42°, so a rainbow can appear throughout the day. In general, the lower the sun stands, the higher the rainbow is. If the sun is higher than 42°, the main rainbow is no longer visible. The right "rainbow weather" occurs when a cold front approaches. This often leads to short showers followed by clearing (April weather). Even during thunderstorms in summer, the sky clears quickly again, making it possible to see a rainbow. Particularly good conditions are in the late afternoon. At that time, the sun is so low that it is not hidden by the last rain clouds over the observer. Additionally, it rains more frequently in the evening than in the morning. Therefore, most rainbows are observed during the hours before sunset. Once the conditions for a rainbow are met, you still need to know where it can be seen. The apex of the rainbow is always exactly opposite the sun. If you think a rainbow might be in the sky, simply look in the direction of your shadow. In this direction, you'll find the apex of the rainbow. The lower the sun stands, the higher the apex. To the right and left of it are the ends of the rainbow. The rainbow's span depends only on the sun's position. The lower the sun, the wider the rainbow. Just before sunset, the rainbow's diameter measures 84°. In addition to the main rainbow with a 42° radius, sometimes a secondary rainbow with a radius of 51° around the antisolar point can be seen. This has the reversed color order of the main rainbow. Sometimes you can see that the area inside the main rainbow is brighter than the area between the main and secondary rainbow. The dark area is also called "Alexander's dark band" in honor of Alexander of Aphrodisias (circa 200 A.D.), a philosopher and commentator on Aristotle. A rainbow can also be created by the moon, although its brightness is very low. The rainbow is formed by the refraction of sunlight in raindrops. The sunlight enters the droplet and is refracted. At the inner wall of the droplet, part of the light is reflected and then exits the droplet with further refraction. Because of the spherical shape of the droplets, the angles of incidence of the light rays range from 0 to 180°. The light amplification is due to more rays being deflected in an angular range of 137.5°-138.5° (180°-42°) than in other directions. In the secondary rainbow, the light is reflected once more inside the droplet before leaving. Since a large part of the light exits the droplet here, the secondary rainbow is much fainter. The color distribution of the rainbow is due to the fact that the refractive index of water depends on the wavelength of the light. The white sunlight consists of light of different wavelengths. Through refraction within the raindrops, the white light is then split into its individual color components. Sometimes additional arcs join the inside of the main rainbow. These interference arcs have a bluish to violet color and arise from the overlapping of waves. Those who pay attention to rainbows will find that they are more common than generally assumed. Often, however, they are only weak and not fully visible.

In the Bible, it is reported that the rainbow became visible in the sky only after the Flood (Matt. 16, 2 and 3). In Greek mythology, the rainbow was the symbol of the messenger goddess Iris. She descended to Earth on it. At the same time, the rainbow was seen as part of her colorful garment. Poseidonios (135-51 BCE), a philosopher of the Stoic school in Athens and other Greek locales, viewed the rainbow as a partial image of the sun and moon, created through the effect of a concave mirror on water clouds. Among the Incas (13th-16th century), the sun and the moon (as the sun's sister) were the main deities. The king himself, the Inca, was considered a god and embodied the sun. The majesty of the sun and its radiance was expressed in the rainbow, which was considered a deity. In Chinese literature, there is also an explanation of the rainbow or the "rain dragon". Sun Ssu-kung, an astronomer of the Astronomical Bureau, said in the 11th century: "The rainbow is an image (literally "shadow") of the sun in the rain and occurs when the sun shines on it. (according to N. Sivin). This remark was passed down by the eminent scholar and administrative expert Shen Kua (1031-1095), who, for example, observed a double rainbow during a diplomatic mission in Kensu in 1070. The Chinese philosopher Chu Hsi (1130-1200) expanded this observation by Sun Ssu-kung and wrote: "The ch'i of the rain [i.e. the atmospheric water vapor or the water droplets] has been thinned, which again occurs because the sunlight shines on it and weakens the ch'i of the rain. As the "first Arab philosopher" during the time of Islam, al-Kindí (801-866) wrote a treatise on the optics of the atmosphere. Ibn al-Haitham (965-approximately 1040) built on this work and wrote seven books on, among other things, experimental and mathematical considerations of light and initial theories of vision as well as a theory of refraction. A shorter treatise encompasses halos and the rainbow, both regarded as reflection phenomena on a concave spherical surface and thought to arise from the "thick and moist air and by clouds". The Islamic scholar Kamãl al-Dín (died around 1320) wrote a new explanation. In it, double refraction is cited as the cause of the rainbow and experimental proof is provided by the application of a small camera obscura with a narrow opening, a method later rediscovered by Descartes. At around the same time as al-Dín, the Dominican monk and later provincial superior Dietrich von Freiberg (1250-1310) wrote a work on the optics of the atmosphere in which similar concepts were developed. He was able to explain the double refraction, namely upon entry and exit, and the internal reflection of the beam in the raindrop, the simple reflection in the primary rainbow and the double reflection in the secondary rainbow. Dietrich barely missed the rainbow theory of Descartes and Newton. This theoretical explanation of the rainbow, still valid today, was first provided by Descartes in 1637 and Newton in 1672 (published 1704) and later in the 19th century by the English physician Thomas Young (1773-1829) and the English astronomer George Biddell Airy (1801-1892). The latter established a "rainbow integral" that allowed the determination of the color intensity distribution. J.M. Pernter performed numerical calculations on this and drew attention again to the work of Young and Airy.

Just as in a delicate cloud arise
Two rainbows with the same color.
When Juno's maid commands it,
and from the inner the outer releases.
(Dante) Truly! A rainbow in the middle of the night!
It is the light of the moon that forms it.
It is a strange and wonderful sign! There are many who have not seen this.
It is double, see, a paler one stands above.
(Friedrich Schiller)