Why is a rainbow an arch?

Answer 1

A rainbow is a portion of a circle. It represents an angle between the line Sun-to-back-of-your-head, and the angle of total internal reflection of each wavelength in the raindrops. Its an optical illusion. As the light passes thought the moisture in the sky its refracted causing the light to change it direction as the light leave the droplets its does so at differing angles these angles.These different colors of light have all slightly different directions and so display each color components of white light. Thus, the angle of bending is different for different wavelengths of light. This band of colors appears in the same pattern as the colors of a rainbow. This means, all the different colors of light (red, orange, yellow, green, blue, indigo and violet) combine to give you what is called white light

You can see circular rainbows sometimes when viewing them from aircraft or high mountain tops where the full area needed to produce a visible circular rainbow has enough droplets.

The rainbow's appearance is caused by dispersion of sunlight as it is refracted by (approximately spherical) raindrops. The light is first refracted as it enters the surface of the raindrop, reflected off the back of the drop, and again refracted as it leaves the drop. The overall effect is that the incoming light is reflected back over a wide range of angles, with the most intense light at an angle of about 40-42 degrees. The different colors (wavelengths) of light have different refractive indices which cause them to bend unequally. Thus, a rainbow is arc-shaped.

We don't actually see the full circle because the earth gets in the way. The closer the sun is to the horizon, the more of the circle we see. Right at sunset, we would see a full semicircle of a rainbow with the top of the arch 42 degrees above the horizon. The higher the sun is in the sky, the less of a rainbow is visible above the horizon.