Rainbows are an impressive natural spectacle since living memory. Among the first descriptions of rainbows there are those in the Bible (Genesis 9:13). The rescued on Noah's ark watched the first rainbow in the end of the Flood.
One can see this optical rainbow when sunshine and rain come together. The rainbow forms a circular ring with an angle of 42° relative to the observation direction around a virtual center exactly opposite to the sun. All spectral colors appear in narrow bands of intensified light with the colors from red to violet from the outside to inside. Under favorable conditions one can observe a second rainbow at a larger aperture angle of 51°, which is much paler and has the colors in a reversed order. Between the two rainbows there is a darker region, which is called "Alexander's dark band" (see Figure).

From the point of view of physics a rainbow appears when sunlight is refracted and bundled, which leads to the raise of light intensity in a narrow angular range. Looking microscopically we see the light of the sun falling onto many small raindrops. The light is at first refracted by entering the interior of the drops, then reflected at the back wall and finally refracted once again by exiting the drop. The total refraction angle is about 138° and this is at 42° with respect to the center of the rainbow. The different colors of light correspond to different wavelengths of light, which are refracted at slightly different angles, like by a prism, thus splitting the white sunlight into colors (dispersion).

The primary (main) rainbow is caused by refraction and reflection inside a raindrop. The secondary rainbow arises from a second total reflection, which reverses the order of colors and lets them appear paler.

The secondary rainbow is created by those light beams, which are reflected twice inside the raindrop. Therefore it is less intense and the order of colors is reversed. The dark band between the two rainbows is just a result of a redistribution of sunlight, which is focused into the rainbow angles. In physics there is no magic: If light gets brighter in one or two zones, this can happen only at the cost of another zone becoming darker.
So we can summarize that the rainbow is an optical phenomenon, which can be explained only by the wave nature of light.