Why do rainbows appear? What are the differences between primary rainbow and secondary rainbow?

White sunlight actually contains a wide variety of colors, which may be roughly classified as seven colors, namely, red, orange, yellow, green, blue, indigo and violet. Normally, we see the sun in white color. After rain, there are still some tiny water droplets remained in the air. If there is sunshine a white sunbeam will be reflected and refracted by these tiny droplets. Different colors of light have different refractivity. They will be reflected in slightly different directions inside a water droplet. If we observe the sky from different angles of elevation, we will see different water droplets reflecting out different colors of light. A rainbow is formed (Fig. 1).

Both the primary and secondary rainbows are phenomena that formed by the reflection and refraction of sunlight in tiny water droplets. When a sunbeam is being refracted twice and reflected once by the droplet, a primary rainbow will form (Fig. 2 a). If the beam is being refracted twice and reflected twice, a secondary rainbow will form (Fig. 2 b). As the secondary rainbow is formed by one more reflection than the primary rainbow, it is much fainter and rare to see. On the other hand, since the paths of sunbeams in a primary rainbow and a secondary rainbow are different, the colors of the secondary rainbow are arranged in just the reverse order of the primary one (compare Fig. 2 a and 2 b).