Whenever I observed a rainbow formed naturally, I found that it is always arc-shaped. Even if they are artificial, for example rainbow formed in garden while watering the plants, it is always arc-shaped. It can never be observed that the rainbow is a complete circle. Why is it so?
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This is an interesting question with a somewhat surprising answer: rainbows are in fact circular, and we usually only see the upper part!
A simple model for explaining this phenomenon is based on an optical system with an incident axis going from the Sun to any droplet. Using Cauchy's empirical law, the reflection of the light inside the droplet has a slight dependency on its wavelength. But for the visible spectrum, the outgoing light will always emerge at an angle close to 42° from the incident axis, and this indicates the position of an observer that can see this colored light:
Remarkably, this phenomenon has a revolution symmetry: only the angle with respect to the incident axis is relevant. This means that provided that nothing obstructs your vision field, and that droplets are everywhere in the air, you can see a whole circular rainbow. But because the Sun is higher in the sky, half of this circle is usually under your altitude, under the ground, where there are neither the incident rays nor the droplets that would reflect them!
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