How is double rainbow different from a rainbow?

Answer 1

The usual rainbow is the arc of color you see in the sky when light "reflects" off of the droplets in the atmosphere and is typically seen in bright sun after a rain. Sometimes there is a second arc, inside and concentric with the first, that is dim but also has the colors. Indeed, it is rare but the faint indications of a third arc can be seen with good conditions and a bright sun and then forms a triple rainbow.

White light passing into a nominally clear material, like glass or water, will bend, or refract, when it meets the interface. For rainbows the light is traveling from air into water and then back into air. The usual rainbow effect is fundamentally like the effect of light passing through a prism in which case, if the angles are correct, light is split into its component colors and we see the "rainbow" of colors.

The rainbow you see is always when the sun is behind you, so light enters the curved surface of a water droplet, then bounced off the inside surface and then exits again at the opposite side of the droplet heading back towards your eye. Only certain angles of the sun, droplet and eye will actually see the effect.

Now, a Double Rainbow has the light bouncing inside the droplet back and forth. One can even sometimes see a Triple Rainbow, but each set of bounces inside the droplet results in decreased amount of light actually making the bounce (some gets through and does not reflect) so the intensity of the light that forms the second or third rainbow is always much decreased. So, basically, one bounce for the first rainbow, three for the second and five for the third rainbow.

The size of the water droplets where the reflection is taking place does affect the intensity and angle of the light bouncing out, but this all highly predictable based on the simplest laws of optics.

For the experts, I will add that there is refraction as well as reflection going on and this is not actually just a simple application of Snell's Law but that simple approach does get you essentially all of the physics of the rainbow while a full scale light scattering calculation based on Maxwell's equations gives the exact and correct prediction of the rainbow colors and positions.