# What shape is formed by the set of all raindrops which create a rainbow to specific observer?

What shape is formed by the set of all raindrops which create a rainbow to specific observer?

Maybe it's easier to narrow this down and consider it this in parts: what's the set of positions from which a raindrop can refract and reflect a beam of red light in the primary rainbow? What shape does that set form? How about the inner brighter part of the rainbow?

Someone asked me this when I describe why the inner part was brighter, but I'm not sure how to work this out!

One commenter suggested this sketch as an explanation, which suggests the shape is a flat plane.

• Look for rainbow in wikipedia, there is a sketch by Descartes on that question. Oct 29, 2011 at 10:29
• So the shape is a circular plane rather than a three dimensional shape? In other words, for each point of a rainbow, there is only one position a raindrop can be in provide a ray from that point? Oct 29, 2011 at 10:37
• In 1st order analysis its such a plane, if You think of some deviation of angle allowed this plane has some "thickness" in reality of course. I recommend some experimnts with a garden spray nozzle when sun (hopefully) will shine brightly next summer :=) Oct 29, 2011 at 10:42
• Just as a thought experiment then: if I had a nozzle which could produce a thin plane of droplets, then there would be only be a fairly narrow range of distances from the observer where a rainbow could be seen? Oct 29, 2011 at 10:46
• Yes, I'd agree. Early 50ties I remember garden spays which produced a thin layer of droplets. But I haven't seen them since :=( This was a simple upward nozzle, and a kind of cone on top. Oct 29, 2011 at 10:51