Part 5/7:
To further understand the optical phenomena of rainbows, we can calculate the angles involved. The deviation angle typically includes multiples of angles of incidence and reflection that are traced back to the observer. The mathematics behind this can be complicated, yet these relationships help in deriving the angles that yield the bright, colorful arcs we perceive.
For example, when calculating the angles associated with a double rainbow, it's essential to account for how many times light is reflected and refracted within the droplet to achieve the minimum deviation necessary for the brightest appearance. The end results of these calculations yield specific angles that correspond to the vibrant colors we ultimately see.