human
I have heard the explanation of how rainbows come to being by light refraction in falling rain drops. I see how dispersion of the entering white light leads to a range of colors becoming visible. But how exactly does this lead to the bow shape of the rainbow?
gpt
The bow shape of a rainbow is caused by the way that light is refracted, or bent, as it enters and exits raindrops. When sunlight enters a raindrop, it is refracted or bent, causing the different colors of light to spread out, or disperse.

The different colors of light bend at slightly different angles as they pass through the raindrop, with the shorter wavelengths of violet light bending more than the longer wavelengths of red light. This causes the colors to spread out into a spectrum, with red on the outer edge of the spectrum and violet on the inner edge.

As the light exits the raindrop, it is refracted again, causing the colors to bend once more. Because the angles at which the different colors bend are slightly different, the colors are spread out in a particular way, with red light bending at a slightly different angle than violet light.

This causes the light to be separated into a circular arc or band of colors, with red light on the outer edge and violet light on the inner edge. The exact shape of the arc is determined by the angle of refraction of the light, which depends on the size of the raindrops, the position of the observer, and the angle of the sunlight.

Because the light is refracted differently as it enters and exits the raindrop, the angle at which the light leaves the raindrop is slightly different from the angle at which it entered. This causes the light to be bent at an angle of about 42 degrees from the observer's line of sight. This means that the observer will see the rainbow in a circular arc, with the center of the arc directly opposite the sun.