Making sense of the elusive twinned rainbow (in the lab, and in reality) Part 1.

Last week I managed to cast on a screen the image of a twinned rainbow.

It was a somewhat accidental act, but then, in a matter of minutes I learned  how to do it over and over again, first time every time, without fail. That was so because the entire process (from the theoretical one to its practical counterpart) is so simply and straightforwardly coherent that in just about anyone's mind everything about it is instantly accepted and accommodated. Let's see next if you agree with me about that.

In all my images of rainbows that I have thus far produced I used two kinds of tools: a number of different LED flashlights, and three glass balls of different sizes. The flashlights (which ranged in power output from perhaps a mere 4 or 5 lumens to a mightily blinding 600) were basically of two different kinds again. One of those had either the LED emitting freely and directly from the front line (so to speak) or otherwise from a 'back' line (if you will) due to an all enclosing hood. (See picture below for a much more eloquent depiction, please.)

Now, let me say this right away: these types of flashlights will not produce an image of a twinned rainbow. In order to get an image of a twinned rainbow a flashlight of the either type below is an absolute necessity.

The LED of the flashlight on the left is situated at the back of an ellipsoidal chamber, which is divided into two unequal parts by a circular kind of wall. The LED on the right is situated at the end of a truncated conical reflective surface.

And now, with everything above being hopefully clear, let us create an image of a twinned rainbow.

There is no need of me to tell you anything about angle of incidence, just as there's no need for you to try to orient your light at an angle as close as possible to the one in the picture, by the way. You will get an image twinned at the top from just about any angle, other than one running perpendicularly to the glass ball. The only difference you'll see with every new angle will be the points where the twin bow merge with the primary bow. (See the examples below.)

If you position your light to shine perpendicularly to the glass ball, on the other hand, you will no longer get an image of a twinned rainbow but the image of what should be called a twin rainbow, instead. (See below.)

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The first clue about how an image of a twinned rainbow is made comes very simply from an observation of the glass ball. Look closely at the photos shown below.

Look at the two overlapping caustics in each picture. Both of them are pointing in the same direction (red end forward, blue end backward).  That means that they are related and originate from a common source. The broader, well-defined and properly aligned one is responsible for the primary bow; the narrower, misaligned one is the generator of the twinned bow. Normally at that point there should be only one caustic present--the primary one. What is the cause of the twinned caustic, then? The answer to that question is easily extracted from the two pictures below.

The first picture shows the fields of light generated by the two types of flashlights I had shown you earlier and specified that they can't produce images of twinned rainbows; the second picture shows the fields of light that are typical to the two types of flashlights, also shown earlier, that are capable of creating images of twinned rainbows. You can extract the answer we were looking for on your own now.

A close inspection of the glass ball has become an absolute norm for me, and now I want to show you what an amazing catalogue of information is always on display for an observer's hungry eyes.

This is a view of the glass ball's back. Notice the copy of the twinned bow in the inverted image at its centre. Behind it there's the secondary bow, and in between is Alexander's Dark Band. The most amazing thing about that secondary rain-bow I never seen being discussed, or even mentioned, by any mainstream physicist. The most amazing thing is the sheer fact that this particular rain-bow is both a primary rain-bow as well as, equally, a secondary one. It is a secondary one from this perspective, and a primary one if you look at it from the other side--which is usually dubbed the front of the drop. It is also the one that's casting the image of the rainbow on the wall. I said 'also' for very good reasons, which for here and now I shall leave unmentioned.

In the picture above notice the three bows displayed at the centre of the glass ball/drop, although the image on the wall is that of only a twinned rainbow. There is a very good reason why not a tripled rain-bow is cast on the wall, which is visibly manifest in the maximised picture below.

Look closely at the secondary bow.

Self-explanatory.

That's all, for now. Come back next weekend sometime, though, and I will share with you the second part of this new saga.

Hooroo.