The following illustration shows a light beam passing a big raindrop with all the important effects like refraction, dispersion and reflection at the round surface of the drop. However, the reflection is less then 100%.
The incident light beam is refracted when entering the raindrop and reflected at the back surface of the water drop. The next interaction with the surface further splits the beam into two parts. The refracted and dispersed part that passes the surface leads to the primary rainbow. The other part is again reflected; when it meets the surface next time, a part of it can exit the raindrop and cause the secondary rainbow.
The menu in the following applet offers the choice of different combinations of primary or secondary rainbows and of the transmitted light (the part of light, which is not reflected). Furthermore, you can select the colors of light red, yellow, green and blue and study their behavior. If you activate the automatic performance you see the sunlight coming from the upper half of the picture. With the slide on the left side you can choose any desired light direction.
The intensity of the primary and the secondary rainbow is shown at the bottom. The highest intensity is seen when the light beam meets the drop at its edge.
The automatic performance demonstrates that the primary rainbow occurs with highest intensities at about 42°. The secondary rainbow occurs only in the area between 51° and 180°, with its highest intensity at the limiting angle of 51°. No light is, however, scattered into the area in between the angles of 42° to 51°! This is the reason for "Alexander's dark band" between the primary and the secondary rainbow.