(Click on the images to enlarge)
Images in the previous pages were seen in a single drop of water. In order to understand how a complete rainbow is formed in the sky we must produce the same necessary conditions as in a real rainbow phenomenon. These include that the light source (the Sun) is behind the observer's back, and in front of him a multitude of falling raindrops, a rainfront, upon which the light shines.
Here we have an observer sitting in front of a wall with a bright spot light behind him. An assistant holds the galss sphere near the wall, letting it "drop" along side it. The sitting observer calls "mark" each time he sees the two light source images merge into a red spot of light on the glass sphere. A red tape is fastened to that spot on the wall. After a strenious while of drop "dropping", there appears, as a consequence, an arc of red tapes on the wall. We thus understand that in these directions the observer can see the red spots of light in the falling raindrops as they pass through that region in the sky. Some raindrops would be nearer some further. The direction is substantial! As there are millions of raindrops falling in the sky following close to each other, the appearance is that of a stationary rainbow arc in the sky.
Here we have presented a falling drop of water as it passes a part of the rainbow arc, illuminated by the Sun. Images of the Sun, as we have seen earlier, can be observed in the drop. When above the rainbow arc, one image of the Sun is visible in the upper left edge of the drop (the 'direct glare' from the front surface of the drop). As the drop reaches the red area of the rainbow arc, a red spot of light appears in its lower right edge. As the drop descends, the red is changed into yellow, then green, blue and finally violet. After that, two, mostly colorless images of the Sun are seen in the lower right edge of the drop. As the drop descends more, the image that is situated at the extreme right edge of the drop disappears leaving one Sun image on the right and the direct glare on the left visible as long as the drop falls.
This is the reason why the sky is darker above the primary rainbow (Alexander's dark belt), as there is only one tiny image of the Sun visible in each drop situated in that sky area. Under the rainbow arc there are three images of the Sun visible. One of these images disappears as the drop moves down and away from the rainbow arc. That is why the sky is brighter directly underneath the rainbow and why it gradually grows dim towards the center of the rainbow.
As we observe the rainbow in a landscape, the Sun is always behind our back and the rain drops in front of us. Here we see a perfect 'half circle' -rainbow. The Sun is exactly at the opposite horizon, rising or setting. The line from the center of the Sun to the center of the rainbow arc runs through the head of the observer.
Here we have presented the position of the Sun and the rainbow arc in the vault of the sky. When the Sun is at the far horizon, there appears a full half circle rainbow at the opposite horizon (presupposing, of course, that there is a rainfront fully illumunated by the Sun). The highest point of the rainbow arc is then at 42 degrees. As the Sun rises the rainbow arc sinks lower. When the Sun reaches a hight of 42 degrees in the sky, then the rainbow arc disappears at the opposite horizon. Observer is pictured in the middle.
We have thus given a phenomenological explanation for the understanding of the rainbow phenomenon. In this we have followed Goethe's way of "taking part" in the phenomena by remaining within the sphere of the observable. We have chosen images and colors as such as the objects of our study (instead of theoretical entities such as "rays" or "waves" of light). Yet, we have come to the same conclusions as mathematical physics. The phenomenological way, of course, lacks the exactness of a mathematical study, yet it is based on well grounded philosophical premises in its exact presentation of that which appears. Both ways are possible and combined they give a more wholistic and comprehensive view of reality.