How does a rainbow form?
A rainbow appears when sunlight is refracted, internally reflected, and separated by wavelength in water droplets. The usual geometry places the Sun behind the observer and droplets ahead. A rainbow is not a fixed object suspended in the sky.
Angular separation of colors
Different wavelengths refract by different amounts. The primary bow involves one internal reflection, with red outside and violet inside. An additional internal reflection produces the fainter secondary bow with reversed color order. As observers move, different droplets send light toward their eyes; two observers do not view precisely the same group of droplets.
Why is an arc usually visible?
The geometry corresponds to a complete circle, but the ground usually hides its lower portion. Elevated viewpoints or aircraft can reveal more of it. Droplet size affects color definition, and very small droplets can produce a pale fogbow. Because the bow depends on viewpoint and illumination, its end cannot be reached by walking toward it. Looking directly at the Sun is unnecessary.