From Disney Research (who knew?)
Researchers unlock secret of the rare ‘twinned rainbow’
ZURICH — Scientists have yet to fully unravel the mysteries of rainbows, but a group of researchers from Disney Research, Zürich, UC San Diego, Universidad de Zaragoza, and Horley, UK, have used simulations of these natural wonders to unlock the secret to a rare optical phenomenon known as the twinned rainbow.
Unlike the more common double-rainbow, which consists of two separate and concentric rainbow arcs, the elusive twinned rainbow appears as two rainbows arcs that split from a single base rainbow. Sometimes it is even observed in combination with a double rainbow.
It is well-known that rainbows are caused by the interaction of sunlight with small water drops in the atmosphere; however, even though the study of rainbows can be traced back more than 2,000 years to the days of Aristotle, their complete and often complex behavior has not been fully understood until now.
“Everyone has seen rainbows, even double-rainbows, and they continue to fascinate the scientific community,” said Dr. Wojciech Jarosz, co-author of the paper and Research Scientist at Disney Research, Zürich. “Sometimes, when the conditions are just right, we can observe extremely exotic rainbows, such as a twinned rainbow. Until now, no one has really known why such rainbows occur.”
Jarosz and the international team of researchers studied virtual rainbows in simulation, considering the physical shape of water drops, and their complex interactions with both the particle and wave-nature of light. The key to the twinned rainbow mystery, Jarosz said, is the combination of different sizes of water drops falling from the sky.
“Previous simulations have assumed that raindrops are spherical. While this can easily explain the rainbow and even the double rainbow, it cannot explain the twinned rainbow,” he said. Real raindrops flatten as they fall, due to air resistance, and this flattening is more prominent in larger water drops. Such large drops end up resembling the shape of hamburgers, and are therefore called “burgeroids”.
“Sometimes two rain showers combine,” Jarosz said. “When the two are composed of different sized raindrops, each set of raindrops produces slightly deformed rainbows, which combine to form the elusive twinned rainbow.” The team developed software able to reproduce these conditions in simulation and the results matched, for the first time, twinned rainbows seen in photographs. The team also simulated a vast array of other rainbows matching photographs.
The team’s discovery was unintentional. “Initially the goal was to better depict rainbows for animated movies and video games and we thought rainbows were pretty well understood,” said Jarosz. “Along the way we discovered that science and current simulation methods simply could not explain some types of rainbows. This mystery really fueled our investigations.” The researchers now see potentially wider application of their method beyond computer graphics, speculating that, some day, accurate rendering models of atmospheric phenomena, like the one they developed, could have impact in areas such as meteorology for deducing the size of water drops from videos or photographs.
The research findings by will be presented Aug. 8 in the “Physics and Mathematics for Light” session at SIGGRAPH 2012, the International Conference on Computer Graphics and Interactive Techniques at the Los Angeles Convention Center. For a copy of the research paper, please visit the project web site at http://zurich.disneyresearch.com/~wjarosz/publications/sadeghi11physically.html.
About Disney Research
Disney Research is a network of research laboratories supporting The Walt Disney Company. Its purpose is to pursue scientific and technological innovation to advance the company’s broad media and entertainment efforts. Disney Research is managed by an internal Disney Research Council co-chaired by Disney-Pixar’s Ed Catmull and Walt Disney Imagineering’s Bruce Vaughn, and including the directors of the individual labs. It has facilities in Los Angeles, San Francisco, Pittsburgh, Boston and Zurich. Research topics include computer graphics, video processing, computer vision, robotics, radio and antennas, wireless communications, human-computer interaction, displays, data mining, machine learning and behavioral sciences.
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John Brookes says: “What is the explanation for the sky between the primary and secondary rainbows of a double rainbow being darker than the rest of the sky?”
The answer is obvious.
RADAR types know the difference; it’s in the polarization of the ‘return’:
http://www.radar.colostate.edu/ece/faculty/bringi/pdf/journals/ECEvnb00012.pdf (1974)
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Disney Research is probably exploring rainbows in Switzerland to extract the especially pure colors in the clean air of the Alpes, to use them for coloring their animations. Stop them before they deplete all the rainbows!
Wow, two pieces of great news in one day: the Mars rover landed safely, and I learned that Disney has a research division! So where do I send my resume to for a job at Disney Research? And does LEGO have a research division too?
[REPLY: The answer is, apparently, “yes“. -REP]
I’ve seen a twinned rainbow under just the circumstances described by charles the moderator: at sunset, with a large body of water west of the rainbow. A perfectly satisfactory explanation was that the second rainbow was produced by the reflection of the sun off the water: each falling drop is illuminated by two suns, not one.
This explanation will not apply if a twinned rainbow appears in the absence of a reflected sun, but absent a clear example of such, I’ll bet the Disney Research team is barking up the wrong tree.
They are gonna be finding a lot more interesting stuff when they start exploring the implications of a newly discovered quantum tunneling effect that lets water droplets refract light a perfect 180 degrees. Basically a photon passing within a wavelength of a water droplet can tunnel in one side and come out on the opposite side except going in exactly the opposite direction. This isn’t possible in classical optics. It isn’t in global climate modeling of clouds either. Less reflection in the models. The modeled photons don’t get refracted unless they hit the droplet and when they do they don’t get refracted 180 degrees. End result more energy from the toy model of sunlight and clouds reaches the toy surface of the planet. Probably part of why they predicted 0.3C/decade in IPCC AR1 and we only got 0.14C as of today for the period 1979-2012 (entire satellite record). That 0.14C is falling right now too and if it continues to fall at rate of last 10 years for another global warming since 1880 becomes global nothing since 1880. Ain’t that a hoot?
http://www.scientificamerican.com/article.cfm?id=the-science-of-the-glory
“””””…..John K. Sutherland. says:
August 7, 2012 at 6:02 am
For those few here who may not have noticed, please note that the uppermost of the two rainbows has the spectrum of colors, reversed……”””””
They are supposed to be reversed; and note also that the dispersion between the colors is doubled due to the light ray making a double trip across the droplet, so the colors separate twice as far during the trip through the drop, so they arrive at wider spaced points, (with different angles) when the ray finally emerges. With a triple bow,
The dispersion is even greater, and of course the third bow is even dimmer. I’m not quite sure whether the third bow of a triple is again reversed to the same as the first; I’ll have to think about the cause of the reversals in more detail; the different colors certainly do not cross inside the drop.
And note the picture says the bows were computer generated. It does not say they were simulated from actual scattering by multiple computer droplets.
I suspect that somehow, the Brewster angle is associated with rainbow formation, because in theory for a perfect sphere, external light rays entering the sphetre, cannot be TIR reflected by the sphere. But rays between the Brewster and Critical angles will have somewhat higher reflection coefficients.
What was Follow the Money on?
Gary Pearse,
I am clearly not a pilot…. I didn’t think of that vista! I was imagining a mountain top at sunset or something like that.
And OF COURSE!! the shadow WOULD be in the middle. very cool.
The things I dream of are commonplace to a lucky few.
Thanks, I will look out the windows of my next flight.
Why is the sky below a rainbow lighter than the sky above it?
Hmmmm …
Could not an experiment be performed under ‘controlled’ conditions to verify this, one such as was performed by Walter Lewin demonstrated in a previous field experiment (where he was assisted by his daughter), but this time a swimming pool or a lake might be positioned behind oneself and the sun, with an aid again holding ‘the garden hose’ on the opposite side?
Here is the previous field experiment performed using a garden hose to create a rainbow:
A smaller scale might even use a full-length mirror (with an assistant and a garden hose) which could be re-positioned as needed to develop the required angle …
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Sorry … the Youtube embedding in the previous post did not place the video at the required 41:26 point in the video where the demonstration with a garden hose creates a rainbow …
Please advance the video with the slider until the 41:26 point is reached.
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John Brookes says:
The primary rainbow is due to light that reflects once inside the droplet before getting out. Light that does this gets out at any angle between 0 deg and ~42 deg, depending on where the light ray enters the drop. [The rainbow occurs because a lot of light gets out around the turning point angle of ~42 deg. See this discussion of caustics: http://en.wikipedia.org/wiki/Caustic_%28optics%29 What gives the rainbow its color is the fact that this maximum angle depends on the color because of the variation in refractive index with wavelength is what causes the rainbow to be a colored caustic. See here for more discussion: http://www.ams.org/samplings/feature-column/fcarc-rainbows , although note that in his graph he defines the angle as 180 deg – (my definition).]
The secondary rainbow is due to light that reflects twice inside the droplet before getting out. Light that does this gets out at any angle between 180 deg and ~53 deg, depending on where the light enters the drop.
Hence, below the primary rainbow, the sky is lightened significantly by light scattered by the raindrops, namely that light that reflects once inside the drop. Above the secondary rainbow, the sky is lightened a little by light that reflects twice inside the drop. In between, you don’t have any contribution from light scattered by reflecting once or twice within the raindrop.
“””””…..joeldshore says:
August 8, 2012 at 11:26 am
John Brookes says:
What is the explanation for the sky between the primary and secondary rainbows of a double rainbow being darker than the rest of the sky?……”””””
Joel has it pretty much pegged, and I wouldn’t disagree with anything he said here.
The formation of rainbows is somewhat related to the SCATTERING of light by clouds, which is not exactly a reflection as we usually put it.
The optics of a perfectly spherical lens can easily be studied by ordinary geometrical ray tracing. It was done extensively for some early fiber optic cable input and output connections, many probably still in use.
In the sky of course, any spherical raindrop is illuminated by an essentially collimated beam of light, although in clouds of course such beams can be going in any direction. A full sphere is a pretty lousy imaging lens and has mucho spherical aberration, and other optical aberrations, including chromatic aberration due to the refractive index being a function of wavelength (higher N for shorter lambda.) as Joel mentioned. For most of the incidence angles (about zero to 53 degrees from the radial normal), water has a low reflectance of about 2%. So any ray entering the droplet, in that range, is going to strike the drop again, and about 98% of it will refract back out of the drop. because of the index change with wavelength, the blue rays will refract deeper into the drop. There actually is an imaginary sphere called the R/N sphere concentric with the drop, and all rays penetrate inside thatsphere, which has a smaller radius for shorter wavelengths. most of the rays suffer very little reflection and mostly exit the drop. Rays that barely make it inside the R/N sphere are somewhat more highly reflected at the drop surface, so less escapes. Inside the R/N sphere, one can define a “Brewster Sphere”, and those up on their trig, can probably show that its radius is R/sqrt(N^2+1). Well I didn’t have any trouble figuring that out so nobody else should either.
Rays that pass inside the Brewster sphere are essentially going to be 98% transmitted out of the drop, scattered widely into a very wide angle cone of rays which rapidly disperses, so it doesn’t register much on the eyes.
The rays that pass through the shell between the R/N (critical angle ) sphere, and the Brewster sphere, are a narrower angular range between Ic, and Ib ( arcsin 1/N and arctan1/N) and they are the stuff of rainbows, because they have somewhat higher reflection coefficients at the drop, between about 4% and 100%, so that is the light that does the bounce once or bounce twice (or three times or more) that Joel mentioned, that form either the inner bow, or the outer bow.
So larger real water drops, may not stay spherical and that can have all kinds of unintended consequences; one of which is that rays could enter the drop at a point with a longer radius of curvature, and reflect over to a point of shorter radius, or verse vicea, to a ray permitted entry could actually TIR inside the drop, and create a strong rainbow component.
I’ve never seen the split bow, but have several times seen the complete cloud top circle bow, with my plane centered in the halo at the center. Always comforting to know that that sucker always looks to be in one piece. down there, or at least circumscribingf my weary bones.
As an aside, the rain drop optics also operate in two dimensions on a cylinder lens; AKA fishing line. A fishing line in water blocks sunlight coming from above. That is the line casts a shadow, since most of the rays that hit the line either reflect off the front surface or are refracted into the line, leaving a shadow wake behind the line, into which the lens focussed transmitted light emerges, forming a very high intensity aberrated cylindrical image of the sun, close to the line, from which a widely divergent beam emerges on the down sun side.
A fish under water can’t miss seeing that bright sun image near the line, so it doesn’t matter a hoot whether they can see the line or not; they do see the shimmering brignt sun streak and they do spook off it. An aquaintance who spends more time down below with the fishies, than up here with the humans, has filmed the fishing line sun streak, easily visible to our eyes, and to a trout’s eyes. I did the optical modelling to prove to him that what he was seeing and filming was not Scottish mist; but quite real.
I knew it wouldn’t be long before one of Miles Mathis’ groupies put in a plug for his inane, convoluted theories. For those of you who don’t know, Mathis is known as in internet science crank who thinks pi = 4.0 and that the moon landings and 9/11 were hoaxes. He thinks planes fly because of an invisible and unmeasurable “charge field”, that the Moon is being shrunk by “charge photons”, that the Earth is molten inside because of “charge” and a host of other junk-science concepts. Mathis is not a scientist and has never done the work it takes to become one, which wholly explains his errors in math and science that even undergraduates wouldn’t make. His degree was in philosophy, and he is not known to have taken any college level courses in either science or mathematics. He calls himself the “New Leonardo” and claims to have corrected all the mistakes in math and science since Newton.
Such a pathological absence of humility should be taken as a warning. Mathis is a purveyor of poorly founded theories based on his misreading of research on scientific matters. Mathis resists all efforts to have his ideas tested experimentally, saying he would just prefer to keep writing more papers. Big honking red flag.
Don’t be misled by this delusional person. Get your science from accredited scientists, who at least have to be accountable for their ideas, not from some recluse sitting in a hovel in Taos, NM.