A double rainbow seen from Saguaro National Park in Tucson, Arizona, features a bright primary and a dim secondary as its companion. In the foreground are the giant Saguaro cacti. Credit: Tony Hallas
Rainbows don’t actually exist. There is no way to find the end of a rainbow (or its pot of gold). It is not possible to cross a rainbow as the Norse gods did on the Bifrost, the bridge through which fallen warriors reached Valhalla, or cross one like Dorothy to Oz.
Rather, rainbows and other similar phenomena are truly in the eye of the beholder – or, we might say, in the mind of the beholder. Seeing a rainbow is the result of a cosmic interaction between solar radiation, optical physics, billions of water droplets, and the human brain’s ability to separate white light into the visible spectrum.
It’s easy to understand the awe and wonder – not to mention the myth, religious devotion and poetry – inspired by the appearance of a beautiful rainbow after a storm has calmed. Ancient cultures had their own stories about rainbows, such as the Greek belief in Iris, the goddess and personification of the rainbow.
For much of human history, rainbows were considered tangible objects. But now we know that these beautiful atmospheric apparitions are exactly that: visions caused by nature and physics. As the French astronomer Camille Flammarion said, the effects of light “produce a thousand optical phenomena, always curious, often fantastic, but all explainable”.
Now we can see clearly
Learning the truth about how sunlight interacts with the atmosphere to allow us to see rainbows took hundreds of years and much investigation.
The great Arab scientist Hasan Ibn al-Haytham, known in the West as Alhazen, performed revolutionary work in the field of optics in the late 10th and early 11th centuries. He experimented on light scattering and suggested that rainbows formed when sunlight hit the concave surfaces of clouds. Around the same time, the Persian mathematician Abu Sad al-Ala’ Ibn Sahl described the laws of refraction.
Building on Alhazen’s work, in the early 14th century the German Dominican friar Theodoric of Freiberg began experimenting with flasks of water to simulate drops. He realized that light was bent – refracted – and then reflected and refracted again within drops of water, while the Islamic mathematician Al-Farisi, also known as Kamal al-din, was the first to determine that colors of the rainbow come from white light. In 1621, Willebrord Snel van Royen (also known as Willebrord Snell), a Dutch astronomer and mathematician, rediscovered Ibn Sahl’s law of refraction, now known as Snell’s law. René Descartes, a contemporary of Snell but working independently of him, also studied refraction in water and provided an accurate mathematical explanation of the rainbow.
Then, in 1666, Isaac Newton had a lot of time on his hands. Cambridge University had closed its doors due to a plague epidemic. While at home, he performed one of the most famous experiments in physics. In a dark room, he passed sunlight through a prism to study what he would call the spectrum. Newton demonstrated that white light is composed of the same colors as the rainbow, ranging from red to violet. His discovery was the culmination of the work of those who had studied these phenomena before him.
Ingredients to make a rainbow
To see a rainbow, four conditions are necessary: the sun must only be at a certain height above the horizon, it must shine through clouds, there must be raindrops in the atmosphere, and you must look directly in front of the sun. If all these criteria are met, you will see one of the most beautiful places in nature.
Rainbows are never seen when the sun is high in the sky. This is due to the angles at which light is refracted when it enters a raindrop, reflects off its inner surface, and is refracted again when it exits the drop. The end result is that the light emerges from the drop more concentrated near the maximum angle of about 42°, with its colors slightly dispersed, forming the primary rainbow. This rainbow appears to surround the antisolar point – the point opposite the Sun – at an angle of 42°.
Consequently, for the rainbow to be visible, the Sun must be 42° or less above the horizon. If it’s higher, you’ll have to be higher too – on a mountain or in an airplane – to see the light at the angle where it emerges from the raindrops.
Most commonly, a rainbow is seen as a single arc with colors ranging from red at the outer border to purple on the inside. We see red at the top of the rainbow because it is bent at the lowest angle. Blue and purple are the most bent and appear at the bottom of the bow. Usually the primary arc is described as seven colors, represented by the acronym ROYGBIV: red, orange, yellow, green, blue, indigo, violet. But depending on the intensity of the rainbow, you may see more gradations between each color.
Sometimes a secondary rainbow can be seen above the primary bow. Because it is caused by further reflection within the raindrops, less light emerges, resulting in the secondary rainbow being only a tenth brighter than the primary rainbow. Also, due to the number of reflections, the colors in the secondary arc are reversed. The sky between the two arcs appears noticeably darker than the sky above the secondary arc and below the primary arc. This phenomenon is known as Alexander’s Dark Band, named after Alexander of Aphrodisias, who described this strange phenomenon in the 3rd century.
If conditions are right, a third, or tertiary, rainbow can be seen above the secondary one. It is even weaker than the secondary and is quite rare. In The Atmosphere, Flammarion describes many other extremely unusual types of rainbows. It tells of Edmund Halley’s observation of “three arches, one of them… reflected in a river. This arch first intersected the outer arch so as to divide it into three equal parts. As the Sun set toward the horizon, the meeting points grew closer. Soon only a single arc was seen, and since the colors were in reverse order, pure white was formed from the superposition of the two series.
Personalized rainbows
I was once asked to speak at a friend’s Unitarian church while the minister was out. He told me I could talk about any topic I liked. The title of my “sermon” was “Everyone Sees Their Own Rainbow.”
When you see a rainbow, your eyes are at the apex of a cone formed by light rays being reflected by raindrops that are at a 42° angle to the antisolar point, from your perspective. (This cone is cut off by the horizon, meaning that the average observer sees only half of the full circle of a rainbow; the full circle is sometimes visible from an airplane when the horizon is much lower.)
If you are driving when you see a rainbow, it will appear to follow you. This is because your cone of vision is what is making the movement. And if you and a friend are next to each other, you both see your own personal rainbows. Of course, if asked, you will describe them in the same way; your cone of vision, however, means it’s all yours. I’ve always considered it a wonderful metaphor for individuality.
What about someone who is severely color blind? How do they see this atmospheric phenomenon? In the most extreme cases of color blindness, a person can see only 1% of the range of colors visible to someone with normal vision. To most color-blind individuals, rainbows may appear to have fewer hues or appear more muted: red may appear more brown, and green may be an olive tone.
Rainbows in the night
If rainbows are caused by the interaction of sunlight and raindrops, how do we explain the accounts of Aristotle, Amerigo Vespucci, Benjamin Franklin, and others of nighttime rainbows?
These individuals did not have hallucinations. Lunar rainbows, or moonbows, are created by sunlight reflected from the Moon. Moonbows are quite rare because even more conditions must come together to create them.
Moonbows can only be seen when the Moon is full or very close to full, which happens 12 or 13 times a year. The Full Moon is about 400,000 times dimmer than the Sun, so if you’re in an area with light pollution, your chances of seeing a moonbow are almost zero. Just as with the daytime rainbow, the Full Moon must be no more than 42° above the horizon. This means you should look for a moonbow shortly after the Full Moon rises or not long before it sets. And, of course, droplets of water must be present in the atmosphere. If all these conditions are present, you may see a faint thin moonbow in front of the Full Moon.
Our perception of color decreases at low light levels. The color receptor cones in our eyes need a fair amount of intensity to start distinguishing colors. Even though all the colors of the rainbow are present in a moonbow, it usually appears pale white to the naked eye. Photographs, however, can capture colors. And don’t confuse a lunar halo, which is a circle around the Moon formed by light refracted by ice crystals, with a moonbow. The lunar arc is always opposite the Full Moon.
A continuous fascination
Rainbows have long been the subject of myths and stories, art and music. And despite our modern scientific understanding, they remain part of our culture.
Even though the rainbow is only in our mind’s eye, it is as real as the light of the Sun and the water of the Earth, providing us with a wonderful cosmic connection.
