Part 4/7:
The formation of a double rainbow involves more intricate light behavior. The additional light rays that contribute to the secondary rainbow undergo two internal reflections within the water droplet instead of one, as seen with the primary rainbow. This geometric complexity results in a secondary rainbow that is fainter and its color sequence reversed due to the difference in refraction angles of light during each reflection.
When analyzing these intricate reflections mathematically, one can derive a series of angles and relationships. The deviation angle of light entering and exiting the water droplet can be expressed through Snell's Law, establishing the relationship between the angle of incidence and the angle of refraction.