On 31 December, 2023, a double rainbow was visible over Old Sarum.
How do the two spectra differ in a double rainbow and why is the arc of sky between them darker than elsewhere?
The lower is the primary rainbow, the higher the secondary and the colours are reversed. Sun (white) light enters each raindrop. Each drop is a prism and the light is bent or refracted, different colours by different amounts. This then hits the back of the raindrop and some of that light is reflected back within the drop, then is refracted again on exiting the drop, to reach our eyes, as a colour. Sometimes it is reflected from the back of the raindrops twice. The second reflection means the colours are reversed.
We only see one colour from each raindrop, those higher in the sky only allow red light to leave them, those lower, violet in the primary rainbow and all these in between give the range between. Red light is refracted at a smaller angle then violet, it is bent less. In the second rainbow, violet comes from the higher and red from the lower raindrops, reversing the colours. The refracted light does not escape the drop after being reflected a first time but goes on to be reflected a second time. The sun has to be behind you and the rain in front of you.
Double rainbows are commoner early or late when the sun is low. The dark area between them is Alexander’s Band. No scattered light leaves the raindrops between the two bows to reach our eyes. Furthermore the primary bow makes the sky inside and the secondary bow the sky outside, lighter.