Category Archives: theory

A single water drop

A slight-projector and a singel water drop shows a lot of bows. Here you can see the primary, secondary and tertiary bow.

The distance between the water drop an the projection backside (white paper) is 30 mm, waterdrop an light source has an diameter of 2 mm.

Photo taken on 28.07.2011 on my desktop 🙂

Author: Michael Großmann, Kämpfelbach, Germany

High order bows

A rainbow is a product of millions of falling raindrops interacting with sunlight. A single reflection form the primary bow, a double reflection forms the secondary bow. However, under ideal conditions there can be many more orders of reflection. As shown above, five, six and even ten internal reflections can be observed. Moreover, it’s theoretically possible to detect twenty internal reflections, but the problem is to produce a perfectly spherical water droplet. The drops I used for this experiment were formed artificially. The light source is a 5 mW green laser pointer. Note that the bright spot at left center is the laser illuminated water drop.

The third and fourth order reflections aren’t shown here because they, along with the seventh and eighth order reflections, are positioned on the other side of the picture in the direction of the light source. The primary and secondary bows will be viewed in the direction you’re facing opposite the sun The fifth, sixth, ninth, and tenth order reflections are also in this direction. However, the third and fourth (as well as the seventh and eighth) order reflections can’t be seen because they’re behind you.

Under exceptional atmospheric conditions it may be feasible to see the third and fourth order bows if you’re facing the sun, but they’re quite faint. A third order bow, for instance, is one quarter as bright as a primary bow. A fifth order rainbow is only about one tenth as intense as the primary bow.

If you need more information about the experiments with high order bows, you can read this pdf.

Nikon D40X, focal length 18mm, 100 ISO, 2,5 sec. at f/6,3

Author: Michael Großmann, Kämpfelbach, Germany

Tertiary Glass-Sphere Bow

I have discovered a spectral reflection phenomenon inside a transparent plexiglass-sphere. The phenomenon, of which I am almost sure it is NOT the equivalent of the Primary or Secondary Rainbow, is in fact the equivalent of the Tertiary Rainbow, visible as a bright illuminating spectral colored ring all along the limb of the sphere. To see this ring, one should look “from behind” the sphere, toward the sun, with the sun “in front” of it (appearing exactly “in the centre” of the sphere).

The photo show the sphere with appearance of the red component of the spectrum. The distance of the observing eye (or camera’s lens) to the sphere is VERY important, because the focal point of the ring is not a point, it’s a spectral colored line (red at the far end, blue at the near end).

As far as I know, no one has ever observed or photographed the ring-like appearance of, what I call, the Tertiary Glass-sphere Bow (which has a focal point or “line”, behind the globe!).

Author: Danny Caes, Ghent-Belgium

Perigee Moon

This photo was taken by Claudia Hinz at the evening of Jan. 11th, 19.35 CET from Mt. Wendelstein (1838m), Southern Germany. The full Moon in this night was extra bright. Dr. Elmar Schmidt of the SRH University of Applied Sciences in Heidelberg, Germany, used an absolutely-calibrated photometer to precisely measure the moonlight and found it more than 50% brighter than that of a typical full Moon.

1. The Moon was at perigee, the side of the Moon’s elliptical orbit closest to Earth.

2. The Earth-Moon system was near perihelion, the side of Earth’s elliptical orbit closest to the sun. Extra sunlight increased the reflected luminosity of the Moon.

3. The Sun-Earth-Moon trio were almost perfectly aligned. This triggered a strong opposition effect an intense brightening of the lunar surface caused by the temporary elimination of normal shadows.

4. The weather conditions were optimal for photometry due to the clean and dry arctic air (its relative humidity being less than 10% at the moment of the photo). This resulted in only clear air scattering of moonlight with no extraneous glare as evident in the completely blue night sky. The brightness of the mountain landscape was additionally increased because of the reflection from the snow.

Elmar Schmidt details the relative contributions of each factor in his full report.

Authors: Elmar Schmidt & Claudia Hinz

Glass Bead Rainbow on Kitchen Table

The observation of a rainbow in glass beads on, respectively next to, a fresh route-indicator in a street I made by chance made me think about studying the effect also in the light of a street lamp. But unfortunately the glass beads had been scattered too much by the traffic within a few days. However, also by chance, I learned that glass beads are also used for facing the surfaces of, for example, metal objects, and so I asked our precision tool maker to bring me some…and then I started the experiment.

As a source of light I used a small bulb like those you find in a bicycle lamp, but without a reflector, because the light source should be as similar to a single point as possible. I scattered the glass beads on a black eloxated aluminum sheet (ca. 30 x 40 cm), and the result was overwhelming. Exactly as in the experiment made by Christian Fenn, the bow can be studied under different geometrical conditions when using a laser and a rotating mirror. The easiest way is to realize the reversed geometry just as otherwise the shadow of the head would be rather large as distances are small. Just put the metal sheet on a table, hold the lamp above it and look at it using different positions of your head. I also took some photographs after having attached the lamp to a mounting. This also shields the direct light. The first supernumerary is also visible, and like in the rainbow caused by water, a polarisation of light can also be proved. (1 2 3)

Seen through a microscope, the glass beads look like this:


I estimated the average radius to be at about 50 micrometers with an average variation of about 15 micrometers. But there are different sizes available. Similar to water drops of that size, the colours are rather blurred (this is especially obvious when you look at a glass bow in sunlight). The spectrum of light coming from a bulb is also rather “red” which causes the strange colours of the pictures.

As I was very fascinated by that phenomenon, I also calculated some simulations using the Airy-theory for glass beads (I could reuse some parts of the original text about the twinned bow for this). And in order to show the phenomenon from the observer´s position, I could use the text on halos on snow covers (so after 10 years the circle is closed…). An imaginary depiction seen from above obviously shows the “intersection through the apple”, but as far as I know, nobody tried to explain the different width of the colour bands up to now. Tis effect becomes very obvious when “opening the inner bow by merging with the outer one” (This is very difficult to describe; you must have seen it). However, the geometrical data of the simulation are not exactly the same as in my observation because I did not execute any measurements while photographing.

Left: Seen from above with the observer´s position in the centre of the picture
Right: Gnomonical projection from the observer´s position (“simulated photograph”)

Author: Alexander Haußmann, Hörlitz, Germany

Reverse Lamp-Rainbow

On August 31st at 01:00 I took some long-time exposures of the Westerhever Lighthouse in Nordfriesland (Germany). It was raining a bit but this didn”t matter because I wanted to display the rays of the lighthouse. Home again I reviewed the photos and was a bit surprised about a kind of arc, originating at a point in height of the lantern room and sloping downwards until it ends +/- horizontal (see pictures 1 2 3). I thought it could be a type of refraction phenomena but I couldn”t explain to me what is was exactly. So I placed the pictures in the Meteoros-forum. Mark Vornhusen and Christian Fenn told me, that this arc is a type of rainbow called “reverse lamp-rainbow” and that these photos are probably the first displaying this phenomena. Both a 42 degree arc as well as a 51 degree arc are to be seen at the pictures.

The rainbows originates from the horizontal Lighthouse-born lightplain cutting the hull of the “Minnaert-cigar”, an apple like shaped figure that describes all those points in which light coming from a source of light is reflectet in an angle of 42° respectively 51° to an Observer. In case of an usual source of light at every point of the Minneart-cigar a rainbow is being generated. But because of overlaying of these rainbows the colour-addition leads to a white light and no rainbow can be seen. However the thin light-layer of the lighthouse-beam only allows forming of rainbows at a small window of the minnaert-cigar and the rainbow becomes visible.

Author: Achim Christoph

Flag corona

Light diffraction doesnt only originate from aerosols like little water droplets or pollen floating freely in the atmosphere, but also from so-called diffraction gratings. These consist of a large number of equally spaced holes or slits, from which the light rays interfere and form an interference pattern. In this example, which I photographed in the beginning of April, the thick woven fabric of the European flag serves as a diffraction grating and shows a beautiful corona.

Author: Claudia Hinz, Brannenburg, Germany

Polarized fogbow in car headlights

I spent the past summer at Langmuir Laboratory on the Magdalena Mountains, in southwest-central New Mexico (USA) at an elevation of 3.2 km. The purpose of this was thunderstorm research. The monsoon here was unusually wet and on several days and nights the mountain laboratory was actually foggy. This is relatively rare considering the New Mexico climate. I took this opportunity to view polarized fogbows in my car”s headlights, and on September 2nd, I was particularly successful.

When I programmed a Mie simulation algorithm late last year and plotted a polarized fogbow on my screen, I was surprised that the polarized bow looked as it did, with the typical Brewster”s angle ”gap” in the main bow for parallel polarization. How excited I was to see that the actual fogbow indeed looked like the simulation! I had never seen it before in nature.

I am sure this has been done before by someone else, but I thought I would post the images anyway.

I covered up one of the car”s headlamps as to not have a double bow. I positioned myself about 50 meters in front of the truck, which I had parked on a slight inclination so the bow would be better visible against a featureless sky and be more complete. The fisheye lens was equipped with a polarizer at the place in the lens where the rays go parallel.

The simulation I made earlier, for a 10 micrometer radius droplet. It looks sharper because I assumed a point light source, assumed a monodisperse droplet distribution, and it was not divergent light. It is not a perfect match either considering the placement of the supernumeraries: probably the droplets in the actual display were a bit smaller. Because of the divergent light source, and because I don”t know the distance to the truck accurately, I doubt I will ever be able to accurately tell the actual droplet radii in the display.

The polarized glory was also obvious, but my shadow was blocking most of the part that was most polarized. I am including the unpolarized glory here.

The close-ups of the polarized and unpolarized fogbow were made with a 24mm/2.8 lens. The camera was a Canon 300d (modified version – i.e. with IR filter removed). I did not need to adjust the brightness and contrast much to get the results as displayed here. The fogbow had good contrast by itself.

About 10 days later I documented a natural fogbow in sunlight from the laboratory, through a polarizer. I photographed that with film; I have not processed those photos yet.

[Posted by Harald Edens]

Divergent Light rainbows

Fogbows have a similar origin to rainbows. For this reason, Christian Fenn, who had previously photographed fogbows made by divergent light, decided to attempt to image a divergent light rainbow. On 19th April in Hammelburg, Bavaria he managed, in pouring rain, to image a rainbow formed by light from car headlamps.

A divergent light source can actually produce a multiplicity of rainbows, not only of angle 42° but at larger angles also. The net result is that the bows overlap and a discrete coloured arc is no longer visible. Another negative factor is that the rainbow cannot develop a high intensity like those sourced by the sun because only a narrow range of rays fall on the “rainbow cone” having its tip at the observers eye. To see a divergent light bow it is necessary to be far away from the light source so that its rays are as parallel as possible and develop a bow of sufficient contrast.

In the photograph the divergent light bow is wider horizontally than vertically. This is because the two car headlamps each form bows and so produce an apparent broadening.

Here is an article from Christian Fenn about this topic.

Seawater and other bows

Günther Konnen has drawn attention to this famous image showing disconnected rainbows. J Dijkema imaged it in the Pacific Ocean.

The upper primary bow (with a fainter supernumerary) was formed by falling rain.

The lower bow was made by drops of seawater thrown up by waves against the ship’s side. The seawater bow has a slightly smaller radius (by about 0.8°). The difference would not normally be apparent but here it is obvious by comparison with the rain water bow.

Seawater, because it contains dissolved sodium, calcium and magnesium salts, is slightly denser than pure water and also has a greater refractive index. The lower diagram shows two minimum deviation rays going through spheres of different refractive index to form primary bows. Seawater and rainwater are too alike to show clearly distinguishable rays and so instead, ray paths are shown for a water sphere (n = 1.33) and a glass sphere (n=1.51).

As the refractive index increases, the incoming ray that forms the primary bow (minimum deviation) moves inwards to so that if it were undeviated it would pass closer to the drop centre. At a sufficiently large refractive index the ray actually passes through the centre, the deviation angle approaches 180°, and there is no longer a rainbow. Highly refractive substances cannot form rainbows.