When you see a double rainbow, why are they always mirror immages or each other,?

Question

the second rainbow has exact opposite color pattern. What gives?

Answer 1

The second rainbow is due to the light reflecting off the insides of raindrops one extra time. This reverses the order of the colors.

Answer 2

A rainbow is created when the light from the sun gets refracted (from the air to the water), one-time-reflected (at the back of the water drop) and refracted again (from the water to the air). The position of the color in the main rainbow depends of the amount of refraction suffered by each color when they leave the water drop. The wave from each different color in the rainbow has a different frequency and the value of the angle the wave gets refracted when it moves from the water drop into the air depends on the frequency of the wave.
A secondary rainbow is created when there is a secondary reflection inside the water drop. If you trace the rays path in a circle you, simulating what's happening when the rainbow is formed with the sun up in the sky, you will see that the first reflection comes out of the drop at a certain angle (42degrees) and the second reflection will come out at a higher angle (around 51 degrees) and for this reason the secondary rainbow is on top of the first one. The secondary rainbow is a mirror image because after reflecting inside the drop for a second time, the trajectory of each light beam is such that the second refraction will invert the sequence of the colors.