We are all naturally broken people

Asked Why is the rainbow round?

When do you see a rainbow?

A rainbow can be seen on a "curtain" made of raindrops when the viewer has the sun behind them and looks at the rain curtain. This is then the projection surface for the rainbow. The sunlight penetrates from the thinner medium of air into the thicker medium of water - and is broken in the process.

Does that mean that the light beam bends a little when it hits drops of water?

Exactly. And not just once: the refracted light beam is reflected on the "back wall" of the round drop and refracted again when it emerges from the drop. The actually white light of the sun is broken down into its different spectral colors.

So the water transforms the white light into rainbow colors. How does it do it?

The different spectral colors - i.e. the bright colors that make up white light - are not all refracted at the same angle. The angles are related to the wavelength, i.e. the speed of the different colors: blue light is the slowest visible light and is deflected by around 40 degrees, red is the fastest and has an angle of refraction of around 42 degrees, the other colors are in between.

So the bundled white sunbeam finally emerges from the raindrop again as a fanned out colorful ray?

That's the way it is. By the way, this doesn't only work with water. A glass prism also splits white into colored light. Only then it is not a bow.

Aha! Let me guess: So the round shape of the rainbow has to do with the shape of the water droplets?

Correct. The water droplets are small spheres. These do not deflect the light as a straight line, but in such a way that each color forms a cone. Due to the different angles of deflection of the individual colors, the individual colored cones are of different sizes and - like the layers of an onion - are nested in one another. What we see is a section through this cone: an arc of a circle.

But it's a rainbow and not a rain circle ...

Yes, from the very top - for example from an airplane - we actually see a circle. But only part of it is visible from the ground. At sunrise and sunset you can see a full semicircle, which gets smaller the higher the sun is.
Strictly speaking, every person sees their own personal rainbow, consisting of many reflected light rays that come from millions of different rain droplets and hit the eye of the respective beholder. The neighbor's rainbow comes from millions of other rain droplets.

Sometimes there is also a double rainbow. How does that happen

The weaker, outer rainbow is created when the refracted light beam is reflected in the drop a second time. It then leaves the drop at a different angle, about 51 degrees. This means that colors are exactly the other way around.
By the way, there is sometimes a "moon rainbow" at night. But because the moonlight shines comparatively weakly, it is seldom seen. And since the moonlight is a light from the sun reflected on the moon's surface, it is not pure white. The spectral colors broken in the rain droplets therefore look rather dull and washed out.