Tag: rainbow

How do mysterious Quetelet rings form?

A strange event was captured on camera as a photographer tried to look through the window of a deserted building at night. The lens focused on the dirty window, and the camera flashed on its own. The outcome was a picture of light refraction on glass. It was framed by a rainbow of stripes. When an automobile is parked under a window, the reflected headlight can be framed by the exact same effect. This is an optical phenomenon called “Quetelet rings.”

This photograph above taken through a dirty mirror reveals the rings of Quetelet as slightly curved stripes. The reflex divides the color spectrum at the maximum of zero diffraction. It continuously transitions from blue to red.

The discovery of the effect

The creation of this effect on a window is determined by a thin film of dirt. Because once the window area is cleansed, it no longer shows the colors of the Quetelet rings. Because of this, we can rule out the interference phenomenon, which is noticeable in double-paned windows and becomes more pronounced after cleaning. Adolphe Quetelet (1796–1874), a multitalented Belgian scientist and astronomer, is honored with the moniker “Quetelet’s rings” for his contribution to explaining this finding.

In daily life, we see spectrum-colored rings that look remarkably similar to so-called corona (multi-colored disks). Under the right atmospheric circumstances, they form around the sun or moon and are produced by microscopic particles in the air like dust, pollen, or water droplets. There are times when all you need is a fogged glass to make out a lantern glowing through a ring of bright colors.

It is essential that particles of the same size scatter the light in these corona events. When it comes to the Quetelet rings, this is obviously not the case, since we are dealing with a dust coating produced at random from grains of varying sizes and compositions. Moreover, what we see is a reflection of the light, rather than the light itself. In addition, the colorful rings often do not surround the light reflection itself but rather seem to rotate about some other point, as if the two events were unrelated.

The sunlight streams in through a filthy window and illuminates it vertically. Several ring colors are clearly evident. Here, they are aligned with the zeroth diffraction order.

However, a closer inspection reveals that the monochromatic light spot is located in a prime place. This is the order of zero diffraction. Instead of being in the middle, as it would be in a typical corona, this one may be seen on the outermost ring. On each side of them, a colorful arc was formed by the intersection of the first, second, and higher diffraction orders. When seen in the zeroth order, the colors in the subsequent stripes always flow from blue to red. However, this sequence is inverted when viewed in the first order.

This property is unique to Quetelet rings. These exhibit the usual characteristics of a specular reflection as well. The arcs change direction in opposite directions as one traverses them, and the radii of curvature rise closer to the disk.

The requirements for the Quetelet rings

A car’s headlights leave narrow, crowded stripes on a window. (Image credit: Eva Sidenfaden)

The involvement of small scattering particles is vital in many processes, including the production of the ring effect or corona. Quetelet’s rings are located atop a thin, see-through layer, like glass. A second layer is required for light reflection. The metal covering of a mirror or its back is ideal for this colorful effect.

If two light waves from the same source interact with the filthy window in just the right manner, an interference will happen. A particle of dust on the outside of the window will disperse one wave, which will then be reflected back through the window from the inside.

On the other side, one gets reflected backwards by the same particle before being distributed forwards. Deflecting and reflecting occur out of sync with one another, thus their courses diverge somewhat. The phase difference between them allows the light to be magnified in the eye or cut out on the camera sensor when they overlap.

The formation of the Quetelet rings

Quetelet rings on a dirty surface. (Image credit: Optica.org)

Quetelet rings are formed when two light waves traveling from a point source collide with a dusty mirror. A dust particle first disperses one of them, and then the back boundary layer reflects it. This also applies to the inverse situation. Spectral interference occurs when two or more colors pass through the eye at the same time.

A perfectly symmetrical casing may be seen by looking at its glass front from a perpendicular angle when, say, a spotlight or the sun is shining directly behind you. It doesn’t matter where in the plane the dust particles are located relative to the light source or the observer; as long as they’re all at about the same distance, they’ll all scatter the light in the same manner.

Finally, the maximum amount of zero interference is located in the geometric center of the concentric color circles. However, one blocks at least some of the light from reaching the eye. So, to see the Quetelet disks, people usually tilt their heads slightly to the side. With this change, the radiation source is reflected off of one of the rings, and the system’s center travels the other way.

Quetelet stripes may be created experimentally with little effort. A flat mirror coated with talcum powder or fogged with tiny drops of water can do the trick. At a distance of two to three meters from the mirror, using a light source as point-like as possible (such as a flashlight with the reflector removed) and holding the lamp up to your forehead, you may see colorful stripes surrounding the direct reflection. These rings have a central part whose location changes as the viewer shifts their gaze away from the light source.

December 7, 2022
How does pollution make sunsets prettier?

The luminous sun ball moves towards the horizon and gradually bathes the sky in a breathtaking play of colors: bright yellow, rich orange, and flaming red—a spectacular and very popular scenery. Ironically, however, the most beautiful and romantic sunsets are said to occur not in remote natural paradises, but precisely where the air is dirtiest. The more dust, the more colorful the evening sky, they say. But is this actually true? Or how does it work at all?

Intense colors during a sunset

It all depends on the size of the particles. In fact, particularly intense colors are created during sunset if there are a lot of small dust particles floating in the air, just like small soot particles from car exhaust. When a light wave hits such a particle, it is scattered, i.e. deflected from its straight path. But a long-wave light beam, which your eye perceives as red, is scattered less strongly than a blue short-wave light beam.

The dust particles filter out the last parts of the cold blue from the evening sunlight, and only the warm colors remain at the end. With many small dirt particles in the air, the red tones, therefore, come out more than they usually do in an evening sky, and the red color becomes fuller and stronger.

In the evening, when the sun is just above the horizon, the light rays have a much longer distance to travel through the Earth’s atmosphere. The short-wave light waves collide with particles so often along the way that they are completely lost by the time the light reaches us. What remains, apart from a few remnants, are only the long-wave red light waves, and it is this color that you see in the sky.

Volcanic eruptions beautify the sky

Landscape with the Carriage at the Sunset, Peter Paul Rubens, 1635

Very small dust particles in the air have the same effect on light waves as air molecules. However, when they are too large, they no longer scatter sunlight but absorb it. In this case, they don’t produce beautiful colors but simply darken the sky. Large particles can also reflect light. Then the sky tends to brighten, with whitish reflections.

There are particularly beautiful sunsets a few days after volcanic eruptions, namely when the large ash particles have settled and only the very fine particles remain suspended in the atmosphere. That’s even given researchers the idea to look for past volcanic eruptions in old paintings.

Christos Zerefos of the University of Athens and his colleagues studied many hundreds of paintings of sunsets painted by Rubens, Rembrandt, and other artists. The meteorologists used a computer to analyze the red-green values of the depicted horizons. In fact, according to the researchers, the pictures with the reddest and thus most beautiful sunsets were created in the years that followed a documented volcanic eruption.

September 27, 2022
How Does A Double Rainbow Form?
How does a double rainbow form? The concepts of coexistence, completeness, and also the protection of the natural world are represented by the rainbow’s spectrum of colors. Even though it has been known for a long time how this characteristic sequence of colors comes about, the arch of light has not lost any of its symbolic force for us, nor has it lost its ability to fascinate us. When a double rainbow forms in the sky, it is a remarkably beautiful sight to see. But how does this multiplication even take place?

Formation of a single rainbow

A primary rainbow. (Image: Earth Science Stack Exchange)

Everybody seems to have a soft spot for rainbows, one of the many enchanting natural phenomena. They mostly appear after a rain, thanks to the sunlight that is reflected off the raindrops. The raindrop absorbs most of the visible spectrum of light, reflecting just a fraction of it. The spherical nature of the raindrop concentrates these reflections at a direction away from the Sun that is 138 degrees. This powerful beam of light will then show a rainbow thereafter.

We have to be looking at raindrops at an angle of 138 degrees from the direction of the sun, or 42 degrees from the antisolar point, in order to see the arc of a natural rainbow.

Light undergoes refraction, or bending, as it travels through air and then into water. All the colors of the sunlight seem a little different after passing through water drops.

Dispersion is the process that causes the colors of a rainbow to shift apart from one another. When passing through the droplets, the different colors of sunlight are bent in slightly different ways. Due to the light’s spectral breakdown, we are able to make out the standard color spectrum. Since blue light has a shorter wavelength and is refracted more strongly in the water droplets, the blue band is the first color in the order of the rainbow, while the red band is the most outside one, followed by the yellow, green and blue stripes.

The reason for the 42 degrees

Raindrops’ ability to bend and reflect light from the sun results in the formation of a simple rainbow. There is no “gold treasure” concealed at the end of the rainbow but the direction in which a rainbow can be seen can still be calculated with a high degree of accuracy. All rainbows will always appear at an angular distance of 42 degrees around the point that is directly opposite the sun.

Why does the angle of formation of the rainbow consistently measure out to 42 degrees all the time? When light rays enter a drop of water, the boundary layer that separates the water from the air causes them to be reflected at an angle relative to the direction from which they entered the drop.

$triple rainbow refraction$
Light paths inside droplets. The sequence and angle of a rainbow are determined by surface refraction and the quantity of internal reflections: a regular rainbow on the left, a double rainbow in the center, and a triple rainbow on the right. (Credit: ISTA)

However, because of the laws of physics for the shape of the objects, a reflection that is more than 42 degrees is not conceivable. All of the light rays that ought to be reflected farther than 42 degrees are instead concentrated at this boundary value.

It is not feasible to see a rainbow at noon because the point opposing the sun that is required to create a rainbow is located below the horizon when the sun is high in the sky. When the sun is high in the sky, the rainbow is more horizontal, but when the sun is low in the sky, it is arced in a way that is proportional to its position.

Are There Triple Rainbows? And How Are They Formed?
Formation of a double rainbow

In many cases, in addition to the primary arc, we can also see a paler secondary arc farther out in the distance. This secondary rainbow arc is virtually a mirror image of the primary arc due to the fact that its color sequence is the exact opposite of the primary arc. The light from the secondary rainbow arc, much as the light from the “regular” rainbow, is refracted into raindrops.

But, when the light beam enters the droplet at a certain angle of incidence, a portion of it is reflected not once, but twice at the boundary layer within the droplet. In this scenario, the maximum permissible value for the angle of the second arc is 51 degrees, instead of 42. In other words, the second rainbow arc always forms at 51 degrees.

The number of light rays that have been twice reflected is smaller than the number of light rays that have been single-reflected, which is why the secondary rainbow arc always looks far weaker.

Bibliography
1. Rainbows, St-Andrews.ac.uk
2. “Rainbows, Halos and Glories”, Robert Greenler, Cambridge University Press, 1980.
3. American Mathematical Society. The Mathematics of Rainbows.
4. Gary Waldman, 1983. Introduction to Light: The Physics of Light, Vision, and Color.
September 10, 2022
The Lunar Corona: Origin of the Moon’s Colored Rings
A bright full Moon illuminating the night sky is a sight to see. The gleaming disk contrasts sharply with the inky background. It’s not always easy to tell where one thing ends and another begins, like when the Moon seems to have a dazzling corona around it. Occasionally, the outskirts of this brilliant region may shimmer with a touch of color, creating the impression of a rainbow arc. Yet, what causes this lunar corona?

Astronomer Joseph von Fraunhofer (1787–1826) began looking for a solution to this puzzle around the turn of the 19th century. He had long assumed that the Moon’s coronas and colorful rings originated from Earth’s atmosphere rather than the Moon itself. Then, which is true?

The Formation of the Lunar Corona

A corona is any optical phenomenon caused by the diffraction (bending) of light by microscopic ice crystals and water droplets in a cloud or on a foggy glass surface, reflecting from the Sun or Moon. A corona consists of many colored rings surrounding the celestial object and a central brilliant spot dubbed “aureole.”

Moon’s colored rings, the lunar corona.

Small particles in the atmosphere looked to be the most likely culprit of the lunar corona. Because the Moon’s rays could be reflected and refracted by them. You can conduct an experiment to demonstrate this, in which you spread a large number of tiny glass beads on a glass panel, let a beam of light pass through the beads, and watch the entire thing through a flimsy telescope.

As predicted, in the 19th century, Fraunhofer saw a rainbow corona surrounding the light source. In his 1825 book, the scholar explained, “The colored rings obtained in this way are the larger the smaller the glass beads are.”

Understanding the Lunar Corona Effect

We can duplicate the lunar corona effect with a simple experiment by breathing on a cool window glass and looking through it at a light or candle. You will see rainbows emanating from the center of the beam.

Lunar corona. (Image: Darrybuffin, CC BY-SA 4.0)

Tiny droplets on the window’s surface deflect the light beams to varying degrees, with the amount of deflection varying with the light’s wavelength. Because of this, they disperse into their component colors, creating a rainbow effect. In general, the red rings tend to be farther in than the blue ones, due to their longer wavelength (the same applies to the rainbows). In fact, this is how the Moon’s iridescent lunar rings come to be.

However, we also discovered the reason why the corona surrounding the Moon is sometimes completely white, which is called a “halo.” If the spheres of particles in the air have very different diameters, the individual colors can no longer be perceived. This is because, in each case, the light will be refracted and diffracted somewhat differently. The result is that our eyes will only be exposed to pure white light—everything will be illuminated in a single color.

Microscopic Crystals and Drops

More is understood today about the atmospheric “haze globules” that Fraunhofer first described. These microscopic particles can be found around us in the form of ice crystals or raindrops. They can only be a hundredth of a millimeter in size, however. When compared to the size of the rest of the sky, the water droplets that form a rainbow are enormous. The small droplets in the upper atmospheric layers typically generate a colorful corona. Clouds with a fine, transparent layer, known as altostratus, are most ideal for lunar and stellar coronas.

The Moon’s rays are deflected when they collide with the small droplets or crystals and are reflected back away from their source. This deflection works even on nontransparent particles like fine dust. The lunar corona may be seen even when there is a lot of it in the air, including pollen dust that can be seen with the naked eye.

Sources:
1. Brand, John C. D. (1995). Lines of Light: The Sources of Dispersive Spectroscopy, Gordon and Breach Publishers. ISBN 978-2884491624.
2. Hockey, Thomas (2009). The Biographical Encyclopedia of Astronomers.
3. Cowley, Les. “Corona”. Atmospheric Optics.
September 3, 2022
Are There Triple Rainbows? And How Are They Formed?
The rainbow is an amazing natural phenomenon. The conventional pattern of colorful bands results from the fundamental laws of reflection, refraction, and dispersion. And under exceptional circumstances, a double rainbow may be marveled at. How about triple rainbows, though? Can they possibly exist? Moreover, how do they form?

Formation of the Single Rainbow

A primary rainbow. (Image: Earth Science Stack Exchange)

Rainbows are one of the numerous natural beauties that everyone is in love with. When rain is falling, they emerge when sunlight reflects off raindrops. The majority of the color spectrum of light is absorbed by the raindrop, but a small percentage is reflected. Because of the sphere’s shape, the raindrop focuses these reflections at an angle of 138 degrees relative to the Sun. After that, there will be a rainbow seen in this intense beam of light.

When light travels through air and then enters water, a phenomenon known as refraction occurs, which is the bending of light. Every one of the sunlight’s colors is slightly distorted when it passes through water droplets. This phenomenon, known as dispersion, is responsible for the separation of colors in a rainbow.

In the droplets, the various sunlight wavelengths are each refracted a little bit differently. We perceive the normal color bands as a result of the light splitting into its colorful spectral components. The blue band is positioned on the inside and the red band is on the outside because the blue light has a shorter wavelength and is refracted more strongly in the water droplets.

Moving From a Single to Double Rainbow

A second, fainter rainbow arc can be seen beyond the first one; its colors are reversed so that red is on the inside. This is because the light is reflected twice within the droplet before it leaves.

A rainbow always appears facing a certain direction: It is situated at 42 degrees on the side of the sky that is directly opposite the sun. It is difficult to see a rainbow at noon because this antisolar point is hidden below the horizon when the sun is high in the sky.

But sometimes, in addition to the main rainbow, a second, paler secondary arc that resembles a mirror reflection of the first arc can be observed on the outer. This is due to the fact that its color scheme completely contrasts with the main arc’s. Because the secondary arcs cause two reflections of the photons within the droplet. The intensity of this second rainbow is lowered, and the order of the colors is changed as a result of the double reflection.

The Formation of the Triple Rainbow

Light paths inside droplets. The sequence and angle of a rainbow are determined by surface refraction and the quantity of internal reflections: a regular rainbow on the left, a double rainbow in the center, and a triple rainbow on the right. (Credit: ISTA)

What about the triple rainbows? A rainbow may also split into two secondary arcs. This has always been recognized as theoretically possible. As a result of the sunlight being reflected three times within the droplet, a third rainbow is created. However, this time, the light beams emerge from the drop facing the sun. Therefore, we need to gaze more intently into the sunlight in order to perceive a triple rainbow.

Typically, a triple rainbow will emerge for a brief period of time when it is 40 degrees from the sun and the clouds are darker. The order of colors in the third rainbow will be just like the primary one.

The tertiary rainbow cannot usually be seen since it is only about fifth as bright as the rainbow’s main arc. It is also too difficult to see the third rainbow because it faces the sunlight. Since just five triple rainbows had been reported to science in the previous 250 years, many scientists had written them off as myths. And it should come as no surprise that the first photographic proof of a triple rainbow did not appear in a scholarly publication until 2011.

We have to be looking at raindrops at an angle of 138 degrees from the direction of the sun, or 42 degrees from the antisolar point, in order to see the arc of a natural rainbow.

Interference Arcs and Mirror Arcs

However, according to climate researchers and specialists, the far more typical occurrences of interference arcs and mirror arcs sometimes could be mistaken with a real third rainbow or triple rainbow.

When sunlight reflects off a water surface, such as a lake, the angle of entrance into the droplets changes, creating a mirror arc. Typically, the main arc and the mirror arc cross.

Contrary to actual secondary arcs, interference arcs are located on the inside of the initial rainbow and run parallel to the main arc. They create a string of successively farther-apart replicas of the initial rainbow, each of which becomes weaker and narrower. They are created by the interference—or the superposition effect—of light rays leaving the drop.

Sources:
1. Gary Waldman, 1983. Introduction to Light: The Physics of Light, Vision, and Color.
2. “Triple Rainbows Exist, Photo Evidence Shows,” 2011. ScienceDaily.
3. American Mathematical Society. The Mathematics of Rainbows.
4. Großmann, Michael; Schmidt, Elmar; Haußmann, Alexander, 2011. “Photographic evidence for the third-order rainbow”. Applied Optics.
September 3, 2022