Yes, a full circle rainbow is indeed possible, although it's less commonly observed than the typical rainbow arc.
While we usually see rainbows as arcs, this is simply due to the horizon obstructing the lower portion of the circle. A rainbow is actually a complete circle centered on the antisolar point (the point in the sky exactly opposite the sun from the observer's perspective).
Here's a breakdown:
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The Standard Rainbow Arc: What we normally see is just a portion of the full circle. The ground usually gets in the way.
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Conditions for Seeing a Full Circle Rainbow: To see a full circle rainbow, you need to be at a high vantage point. This could be from an airplane, a tall building, a mountain, or even a waterfall. The key is to have a clear view of the antisolar point and the rain or mist.
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The Antisolar Point: This is the key to the rainbow. The center of the rainbow circle is always at the antisolar point. Because the sun is behind you when you face a rainbow, the antisolar point is directly opposite the sun.
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Why We Don't Usually See Full Rainbows: As mentioned, the horizon typically blocks the lower half of the rainbow circle.
In summary, while rare, a complete circular rainbow is a real and beautiful phenomenon that can occur when the conditions are just right, particularly with an unobstructed view of the antisolar point.