How Do Rainbows Form?

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What is a rainbow?

The rainbow is one of the more spectacular light shows observed on earth. The traditional rainbow is sunlight spread out into its spectru Image of a Rainbow

m of colors and diverted to the eye of the observer by water droplets. The "bow" part of the word refers to the fact that the rainbow is a group of nearly circular arcs of color all having a common center. Typically, we only see a portion of the entire circle, leading to the bow shape.

What makes the bow?

To understand how the bow is formed, we need to consider the path of a ray of sunlight through a single round raindrop. As light enters the raindrop, it is refracted (the path of the light is bent to a different angle), and some of the light is reflected by the internal, curved, mirror-like surface of the raindrop, and finally is refracted back out the raindrop toward the observer.

This schematic represents the path of one light ray entering a raindrop at point A. As the light beam enters the surface of the rain drop, it is bent (refracted) a little and instead of continuing to point D, strikes the inside wall of the raindrop at point B, where it is reflected back to point C. As it emerges from the raindrop, it is ref Image of the path of a ray of light through a raindrop

Image of the path of a ray of light through a raindrop

racted (bent) again into the direction E. The angle created at point D is 42 degrees.

The ray drawn here is significant because it represents the ray that has the smallest angle of deviation of all the rays that can enter the raindrop. This means that much of the sunlight that is refracted and reflected through the raindrop is focused along this path. This is known as the rainbow ray. Since the various colors that make up white light all have slightly different wavelengths, each color becomes slightly separated from the others as the light ray is refracted and reflected. So, rays that strike the raindrop at this angle of 42^o will tend to form a concentrated, strong beam in which the colors will be widely separated. This creates the color bands in the rainbow, with blue along the inner portion of the bow, and red on the outside edge of the bow.

Since the raindrop is circular, the reflection it creates is also circular. We don't see a full circular rainbow however, because the earth gets in the way. The lower the sun is to the horizon, the more of the circle we see. At sunset, we would see a full semi-circle of the rainbow with the top of the arch 42^o above the horizon. The higher the sun is in the sky, the smaller the arch of the rainbow above the horizon. If the sun is more than 42^o above the horizon, no rainbow will be visible.

So, the main ingredients to see a rainbow are the following:

You need to be standing with the sun to your back and the rain in front of you.

The sun needs to be less than 42^o above the horizon.

The sun's rays must be hitting the raindrops to create the rainbow.

What makes a double rainbow?

Sometimes we see two rainbows at once. What causes this? We have followed the path of a ray of light as it enters and is reflected inside the raindrop. But, not all of the energy of the ray escapes the raindrop after it is reflected once. A part of the ray is reflected again, and travels along a different path inside the drop to emerge from the drop at a different angle. The rainbow we normally see is called the primary rainbow and is produced from one internal reflection. The secondary rainbow arises from two internal reflections and the rays exit the drop the second time at an angle of around 50^o, rather than the 42^o for the primary rainbow. This effect produces the secondary rainbow, with the colors reversed from the primary rainbow. It is possible for light to be reflected more than twice within a raindrop, but these additional rainbows are typically never seen under normal circumstances.

Why did people in Ireland believe there was gold at the end of rainbows?

Even as far back as the 17th century, people knew that we cannot see the complete circle of the rainbow, and instead we see only a portion of it, in the shape of a bow. In Ireland, people in the 17th century became fond of saying that one was as likely to find a pot of gold as to find the end of the rainbow. The expression somehow changed, and became a part of mythology.