Refraction caustics (15th of June 2011)

Caustic is an inhomogeneity in, initially homogeneous, beam of light after it passes through a system made of refractive and reflective objects. One can most easily spot the local amplification of light on the surfaces where the part of the beam ends up. I already wrote about the reflection caustics in the post >> Lord of the ring caustics. This post deals with the occurrence of caustic in the transmitted light, in refraction.

Refraction caustic is omnipresent around water. Our conception of the sea is unthinkable without caustics, although people rarely realize this. Multiply connected network of amplified light that dances on the sea floor is part of the visual that we automatically relate to the sea. I intend to dedicate a special post to this sort of refraction caustic, so I won't speak about it here. This post will discuss caustic in a glass filled with pieces of ice, with a little bit of spirit (cognac, whisky) in it. On the image above one can see the caustic effects produced in such a system. These are most easily discerned within a shadow, as torn up traces, "cuts" of light. They originate in the complex shape of the ice cubes.

But, complexity of the refractive object is not a necessary condition for the complexity of the caustic. One can see this on the image above, where the ice cubes are perfect cubes, indeed. Yet, there are five of them, so that the caustic is determined by multiple refractions, each of which redirects a part of the light beam which strikes a particular part of the surface. One can again see that the caustic traces on the table are very complex and torn up.

Ice "cubes" can be more like spheres than cubes. They can be fairly complex shapes, depending on the mold used to freeze the water. An example of a glass with a somewhat more complex pieces of ice is shown in the image above. The caustic is again quite complicated, and in it one can also see the part that comes from the edge of the glass. Irregularities and slight waviness seen in the caustic are very much typical. Namely, even a small irregularity in the surface of the refractive object will be seen in its caustic in an amplified manner - one can easily demonstrate this using the laws of similarity and trigonometry. A detail of the caustic from the image above is shown magnified in the image below.

And if you still didn't get the nature of objects that represent the ice on the two images above, on the image below I show one of these objects alone, together with its caustic.

In the end, the caustic on the same system, but this time the ice "cubes" are perfect spheres, but smaller from the previous cases. That is why a large number of them can fit in the glass (the image below).

In all of the examples shown, one of the problems that needed to be resolved in order to create an image was a setup of the objects so that they do not intersect one another. That problem is perhaps the most obvious in the image above where the number of spheres is quite large so the problem also appears more important. On the other hand, in that case, the ice pieces are perfect spheres and the problem is simplified by this fact.

I dealt with the problem of packing of many spheres in a cylinder in a (partially) scientific context (although I didn't yet publish anything on that). Such packings automatically lead to formation of helix, a spiral pattern that is typical of packing of amino acids in proteins, but also of packing of bases in a DNA molecule. That is why the problem has certain biological and physical background. I used one of the solutions to the packing problem earlier in order to create a fantasy building in the post >> spline mountains. I repeat this image below. In this case, the packing is such that a space surrounding the cylinder axis opens and one can insert another, coaxial cylinder in it, which was done in the image below.

I intend to study packing problems in the future so I hope that I will have an opportunity to explain all that physics and mathematics in some future post.

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Last updated on 15th of June 2011.