This summer I was traveling in Tibet. It was a hot day, and we were moving from the Tibetan Plateau down to the Kathmandu Valley in Nepal, jumping fast from 5,000m to less than 1,500m altitude. We had a stop in the Nyalam, a small Tibetan town of the Shigatse Prefecture near the border, situated at 3,750 meters above sea level. When my sister, with an astonished voice asked me “What’s that up in the sky?”
I had not time to answer as I was already pointing up with my camera to catch the first and only circular rainbow I have ever seen. A few seconds after, with my face still hidden from the camera, I was trying to build up a possible, realistic and credible physical explanation of that phenomenon, not to lose the credit of “all you can answer” optician in front of my sister.
That’s something you have to face every day when you are a scientist: people can ask you whatever they want, whenever they want.
That episode reminded me of a previous one which happened in Norway in 2009. I was traveling with some friends when we saw a rainbow and its second order one. They felt so lucky to see two concentric rainbows, that I had no pluck to tell them that it was the same one!
Both episodes showed me the polyhedric feelings triggered by the vision of a light phenomenon as common as rainbow. From Greek mythology, where Iris is the personification of the rainbow and a messenger linking the Gods to humanity, up to the LGBT movement, whose symbol is a rainbow flag to reflect the diversity of their community, rainbows have been always associated to creation, divinity, good luck, duality, peace, energy and even gates for extraterrestrials worlds. It has probably been one of your first drawings when you were a child. According to the developmental psychologist Jean Piaget, rainbow drawings are typical of the preschool years, when children are approaching realism, but drawings remain fanciful: as ground and sky that never meet at the horizon, or rainbows formed without a drop of rain, as if we want to preserve its magical colorful poetic image from the wet, dark and tedious rain.
By the way, although we have a poetic vision of rainbows, we cannot resist asking what they are. A rainbow is an optical phenomenon caused by interaction of light, normally the sun, with water droplets, normally after the rain. In general, when light passes from a medium to another one, it splits in two parts: one reflected and one refracted. Let us imagine, now, that the first medium is the sky, and the second one is a water droplet. When the sunlight encounters a raindrop, part of it is reflected and another part is being refracted at the surface. When this light hits the back of the drop, once again reflection and refraction happen. And if we follow just the reflected light, it will be again reflected and refracted again when trying to escape the raindrop.
Without entering into too much detail on the physics, the overall effect is that part of the incoming light is reflected back over the range of 0° to 42°, with the most intense light at 42°. This angle is independent of the size of the drop, but does depend on its refractive index. Like on the Pink Floyd cover of the album The Dark Side of The Moon, showing light dispersion in a prism, also in a raindrop the amount by which light is refracted depends upon its wavelength, and hence its color: blue light is refracted at a greater angle than red light, but due to the reflection of light rays from the back of the droplet, the blue light emerges from the droplet at a smaller angle to the original incident white light ray than the red light. That’s why you will always see blue on the inside of the arc of a rainbow, and red on the outside. If you are so lucky that raindrops are big enough, and light reflects twice inside them, you will see a secondary rainbow at an angle of 50–53°. In this case colors are inverted compared to the primary one, with blue on the outside and red on the inside.
For the moment, hoping not to have destroyed your love for rainbows, I just explained you why it is possible to see two concentric and inverted images of a rainbow, like in Norway. They are just the same phenomena, the same rainbow.
To answer to my sister the question about the circular one, we first have to understand why rainbows have an arch-shape. As brilliantly explained on Wikipedia, “rainbows can be seen depending on the particular observer’s viewpoint as droplets of light illuminated by the sun. All raindrops refract and reflect the sunlight in the same way, but only the light from some raindrops reaches the observer’s eye. This light is what constitutes the rainbow for that observer. The whole system composed by the sun’s rays, the observer’s head, and the spherical water drops has an axial symmetry around the axis through the observer’s head and parallel to the sun’s rays. This already explains the circular arc-shape of the rainbow: whatever is the effect of any water’s drop on the observer, rotating around the axis must leave it unchanged. Therefore, the bow appears to be centered on the shadow of the observer’s head, or more exactly at the antisolar point (which is below the horizon during the daytime, unless the observer is sufficiently far above the earth’s surface), and forms a circle at an angle of 40–42° to the line between the observer’s head and its shadow. As a result, if the sun is higher than 42°, then the rainbow is below the horizon and usually cannot be seen as there are not usually sufficient raindrops between the horizon and the ground, to contribute”.
Oops, I think that this means I have no answer for my sister, as one cannot see a circular rainbow if I don’t have the right vantage point.
Looking at the phenomena in Tibet, the first thing I noticed was that the color sequence was the reverse of the rainbow. But…can you say to someone skipping happily that it was not a circular rainbow?! Even if physicists have the responsibility to truthfully describe nature, they should preserve an undefined percent of poetry and illusion in people. That’s why I answered “a kind of rainbow”.
What we saw in Tibet was a halo created by reflection and refraction in hexagonal ice-crystals, instead of water drops. What happens close to the border between Nepal and Tibet is that the warm and wet air coming from the Nepalese subtropical valley goes up, reaching at the Nyalam altitude the cold Himalayan climate. In these conditions it is easy to have ice-crystals formation in the troposphere.
Rainbows and halos both rise from a refraction phenomena. The former between sunlight and water droplets, the latter between sunlight and ice-crystals. Halos can have different shapes (pillar, spots and arc), while rainbows appear as arches. In circular halos, the size is constant, determined by the angle of refraction through six-sided ice crystals. The primary halo is always 22°. If color is visible, it will be red on the inside and blue on the outside. The larger halo at 46° has reversed colors.
Even such scientific explanation does not overshadow the fashion of a sunlight ray transforming itself in a painter’s palette. And if I know what happens, I cannot hide the wonder and joy that I feel all the times that light show me all its colors.
Now that I have the answer for my sister, I start to think who’s next. Which friend will stay with me in front of a rainbow wearing polarizing sunglass? In the meantime, I’ll start to write my answer, hoping to share it with you another time.
Antigone Marino is researcher at the Institute for “Superconductors, oxides and other innovative materials and devices” of the Italian National Research Council. She received her master of science in Physics in 2000, and the research doctorate in New Technologies in 2004, both at the Physical Science Department of Federico II University of Naples, in Italy. Her research activities have been concentrated on the study of soft matter optics applied to telecommunication, with a special interest in liquid crystals technologies.
She works for several learned societies. Since 2013 she is chair of the Young Minds project from European Physical Society. The project, aimed to promote the next generation of physicists, includes nowadays more than 300 young scientists from over 27 Sections in 14 countries.