Rainbows Have No Ends
All rainbows are, in theory, circles. You don't see them as such because the Earth gets in the way! But pilots have noticed full-circle rainbows outside their plane windows, proving that if you get high enough, you can see a rainbow in its entirety. If you're stuck on the ground, however, you can see the largest percentage of a rainbow (around 50% of the circle) by spotting one around sunrise or sunset. You can also create a full-circle rainbow yourself if you spray mist from a hose with your back to the sun.
from Slate Magazine
Key Facts In This Video
When light enters and exits a raindrop, refraction changes its direction by around 138 degrees. (0:07)
If you are high enough above the ground, you may be able to see a full-circle rainbow. (0:39)
Double rainbows are technically called secondary rainbows. (1:23)