Rainbows are both beautiful and rare, but we see more than our fair share of them in Hawaii because our mountains and tradewinds combine to produce rain on the slopes of the mountains. Because of the orientation of the islands, it is not unusual for the low morning or afternoon sun to shine under clouds over the mountains and illuminate rain beneath the clouds.
Rainbows are visible when a bright light source is directly behind an observer who is looking into airborne water droplets. The spectrum of colors appears in a circle around the observer’s shadow. We see neither the shadow if the rain is far away, nor the entire circular spectrum when the sun is above the horizon. The sun must be no higher than 42 degrees or the light from the water drops does not reach the ground.
The spray of a garden hose can create a rainbow, and airplane passengers often see them surrounding the shadow of an airplane. A similar phenomenon called the Specter of Brocken occurs at high elevations when the sun is low and casts your shadow into a cloudbank.
Each water droplet refracts the light of different colors at different angles to spread out the rainbow, which comprises white light. The light reflects off the back inside surface of the drop and exits the front as it spreads out in a cone. The rainbow appears as a full circle of light with a radius of 40 degrees for violet and 42 degrees for red, although we cannot see the entire circle from ground level. A secondary rainbow appears 9 degrees on the outside of the primary.
The secondary rainbow is caused by an additional reflection from the back of a water droplet, reversing the colors. Supernumerary arcs are pale pink or green bands that may form on the inside of the primary rainbow. They result from interference of light waves that emerge from water droplets in the same direction
Although each droplet contains the entire rainbow, you see only a portion of it reflected from each droplet, like the dew that flashes colors from the grass in the morning sun or a diamond in a bright light. To see a rainbow there must be a multitude of drops spanning the diameter of a circular cross-section of the cone whose axis lies directly in line with the sun and the observer.
If you could suspend a single water droplet in space and move around it, you would see the entire spectrum. When you can see the all of the hues of the rainbow, it is because the combined light from a multitude of droplets is reflected back to your eyes at the same place.
From different locations you will see light from different droplets, so no two observers see exactly the same rainbow. This is why the rainbow follows you as you move, and the reason for the legend of the pot of gold at the end.
Richard Brill is a professor of science at Honolulu Community College. His column runs on the first and third Friday of the month. Email questions and comments to brill@hawaii.edu.
