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