If you didn't know, the title is from a poem by William Wordsworth. We'd just made a pilgrimage to his grave in Grasmere and climbed Helm Crag on a showery day. Here are pictures of a rainbow above The Lion rock formation. Notice how big and circular the rainbow appears to be.
Rainbows are a reflection effect. Light from the Sun enters a raindrop and is refracted, which splits the colours as happens inside a prism. Then there is reflection from the back of the raindrop, so the rainbow is on the opposite side to the Sun. I thought it was total internal reflection but apparently not: some light escapes through the back of the raindrop by further refraction but not enough to make a visible rainbow between you and the Sun.
Notice here that there is a double rainbow. The second rainbow is formed when some of the light undergoes a second reflection inside the raindrop. This sends it out at a bigger angle and the second reflection flips the order of the colours.
The huge size of the rainbow can be explained by being so high up. Apparently the rainbow is centred on what is called the antisolar point. I made the diagram below to explain it. In theory a rainbow can be a complete circle around the antisolar point but the fact that the antisolar point is underground means that you can't see most of it. Being so high up on the mountain means that less of the full circle is blocked by the ground and what we saw was more than a half circle. I found a lot interesting stuff and many new types of rainbow for me to spot on http://en.wikipedia.org/wiki/Double_rainbow#Variations
