Rainbows in diverging light
by Christian Fenn, Hammelburg

Part 2

Reversed lamplight rainbows

lamplight reverse rainbow
Figure 5: The possible rainbows behind the light
source lose structure by superimposition
and thus cannot be recognized

After having considered these things, I wondered what would happen if the light would be sent backwards through the rainbow - that means, if light source and observer would change position.

I had simply thought that there where first the lamplight rainbow had appeared (i.e. directly in front of the eye), now the “reversed rainbow” would appear directly behind the lamp. So I imagined that in diverging light there would also a small rainbow appear around the light source. As I had never heard about this bow, I was motivated to make a new discovery, but I did not find that “reversed rainbow”.

When I made a construction later, my mistake in thinking became obvious at once. When I looked at the part of the “apple” (“Minnaert-cigar”) situated behind the lamp, I saw the same part of the “apple” from a completely different position. The addition of all possible rainbows at all angles led to the conclusion that they would extinguish each other. The lamplight rainbow would not appear at 1°, 2°, 3°, and so on and thus would not be visible for me.

Theoretically, the “reversed lamplight rainbow” existed at any point between 0° and 138° (180°-42°), but just for this reason it would not be possible to observe it. This would only be possible if one would be able to perceive such a bow only at an isolated angle. This was impossible, as it would never rain only on a narrow sectional plane.

I forgot about the “reversed lamplight rainbow”

Christoph Gerber's observation

lamplight reverse rainbow
Figure 6: First observation by Christoph Gerber
a) view from the observer's positionintent of reconstruction!!!
b) situation (reconstructed)

gesichteter Bogen = bow seen
erwarteter Bogen = expected dew bow

lamplight reverse rainbow
Figure 7: Second observation by Christoph Gerber
a) view from the observer's position
b) situation seen from above (reconstructed)

Radweg = cycle-track

One month later, I read Christoph Gerber's report about bows he observed at a street lamp. He described two different observations, which however were rather similar to each other.

In his first report Christoph Gerber describes a bow that had appeared behind him in the night and was at the same time situated on the other side of the lamp. The bow seemed to follow him (see fig.6).

In his second report he describes a bow that seemed to have been orientated around a lamp, getting smaller when Christoph Gerber came nearer to the lamp and bigger at a larger distance from it (see fig.7).

Both bows were no typical forms of a rainbow as they changed their size and appeared in direction towards the light source. So at first sight the possibility that Christoph had observed a rainbow here, could be excluded.

The situation is different, however, when you put the regularity of rainbows in diverging light into consideration. I already said above, that in diverging light rainbows can appear around the “antilamp” point and that they do not appear in direction towards the light source just because the “reversed lamplight rainbows” which are theoretically possible superimpose each other, so that they could only be visible at an isolated angle. The isolation of a single angle at a single point, however, cannot be observed in the atmosphere, as in such a case raindrops had to fall only at certain positions.

lamplight reverse rainbow
Figure 8: Reverse lamplight rainbow
Christoph's observation, however, shows such an isolation. As it did not rain when he made his observation, only the raindrops on the grass could generate a rainbow. So the ground was a kind of sectional plane through the “apple of all possible rainbows”, thus isolating some single angles.

According to how this apple is sectioned, an unlimited number of shapes of different bows can come together. They can appear behind the observer, behind the lamp, and also between lamp and observer. The size of the circle is hereby determined by the distance of the observer to the lamp and the height of observer and lamp in relation to the ground. When the sectional plane is flat, up to four circles can appear around each source of light.

The figures 9 and 10 shall illustrate in a rough way how the sectional planes through the “apple” were orientated to make Christoph Gerber's observation possible.

The figure shows how the “apple” becomes smaller the nearer the observer gets to the lamp. So the bow formed by the section becomes also smaller - just as Christoph Gerber described it in his second observation.

radius of lamplight rainbow
Figure 9: The bow visible becomes smaller the nearer
the observer gets to the light source
radius of lamplight rainbow
Figure 10: Graphical illustration of
Christoph Gerber's second observation


Visible rainbows can appear in diverging light. They can only be perceived when the observer stands with his back towards the lamp. If, however, there are raindrops only on a plane, as for example the wet grass, then sections through the “apple of all rainbows” are formed and the “reversed rainbows” from the theory (we also can call them reversed dew bows) can be observed. The thought of the reversed rainbow, which was a bit cocky at first sight, could be confirmed by the observations made by Christoph Gerber and at the same time is an explanation for his observations.