"The rainbow is an optical illusion but if you must, here is how you could calculate it. You need to know the distance you are from the drops of rain that reflect the light of the sun in a prismatic way. The rainbow is the a circle of roughly 40 degrees. Multiply that distance by the sine of 40 and you'll get the radius of the rainbow. Multiply by 2 * Pi and you get the circumference. If you are on the ground and therefore wish to know how long is the rainbow you see as a half circle, you must divide the circumference by two".
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Response last updated by gtho4 on Jun 07 2021.
Mar 25 2015, 8:52 AM
Assuming he questioner meant length in distance and not duration, the answer is that as it is purely an optical effect it does not have a real length at all. I suppose if the observer were to stretch out his arm and point to one end as he saw it, and sweep round the arc to the other end, it would be in the region of 9 feet, assuming a full 180 degree rainbow. In reality all one can measure would be the angle covered by what is visible. As to what the average might be I have no idea, but I have only rarely seen any that approach the full 180 from horizon to horizon. http://www.scientificamerican.com/article/what-determines-the-size/
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