Lord of the rings caustics (6th of March 2011)

This year two students applied to make diploma theses under my guidance. One of the theses is about the application of the theory of stochastic processes in biophysics and econophysics and the other one is about simulating caustics using the method of raytracing. Detailed descriptions of the thematic of both diploma works can be >> seen HERE, but only in Croatian. In this post I will discuss caustic a bit. Caustic is a structure (envelope of rays) in the reflected or refracted beam of light that can be seen on a screen i.e. projection surface. It arises due to a concentration of light intensity in certain regions of space after reflection/refraction, due to characteristic shape of the reflector i.e. refractor. A simplest example is the (idealized) concave mirror in geometrical optics. In that case, "caustic" arises due to reflection of parallel beam of light on the mirror and it is circular when the projection screen is positioned perpendicularly to the optical axis of the mirror. In the focal point, all the light intensity gathered across the whole mirror surface becomes focused in a single point, so that the "caustic" in that limit is a point.

But, for "real" optics, without application of different (paraxial) approximations, caustic is a fairly complex object. The best known caustic is the one that arises due to reflection on the interior of the ring or a cup and it is called the ring caustic. And so began this post. Ring. Caustic. The Lord of The Rings. The lord of the ring caustic. On The One Ring, there is an engraved inscription that can be seen in fire and that, translated from the Black Speech of Mordor to English, says

So I started to think about the ring that I do not wear in "real" life. But, if I were to wear it, what would I want it to be like? And I concluded that the look of the ring is perhaps not that important, but I would like it to be engraved with a saying important to me, with some thought that I could remember in difficult times, turn the ring around my finger, feel the texture of the engraved text, and get courageous.

In the search for those little wisdoms that I would engrave on my ring, I went through the notes I wrote in my computer and, indeed, I found some that I've written in the last couple of years. The saying engraved on the interior of the ring shown in the opening image of this post is:

Golden ring with steel elements (cubes) and ornamented font, appropriate for the author and the age of the saying, is an excellent reflector. One can on the image see traces of light reflected from the steel cubes and caustic in the interior of the ring where one can also see a part of the engraved text that is on the way of light (see below).

The part of the text that can be clearly read is If you work with your hands,. This part of the text twists around the point of the strongest intensity of the reflected light.

The second ring I made (see below) is much less pretentious, and the font that was used to write the statement is intentionally casual, almost childish. The statement, engraved along the wavy path in the ring, is:

This ring is made of silver with a series of vertical golden cuts. The light source is this time in a bit higher position so that the caustic is smaller around the position of the largest light intensity, That the light source is in a higher position can be also seen from the fact that the area of a directly lit region is in this case larger than it was in the case of the ring of St. Francis. I could write a lot about Erik Satie, but I will leave it for some other opportunity.

The third ring I made (below) is perhaps the most elegant of all. It is made of silver with two golden tori/rings on the outer side. Its inscription is:

In Nietzsche's ring (above) one can clearly see overlapping of areas of the directly lit support (wooden table) and the support lit by the light reflecting from the ring interior (caustic).

The fourth ring (below) has an engraved statement of a man who was completely certain that Nietzsche was a madman - Tolstoy. His statement is:

Tolstoy's ring (above) is a golden one with an array of inserted copper spheres and the golden torus in the middle. I wrote about Nietzsche and Tolstoy in my book, >> Problem promatrača (Problem of the observer).

And in the end, fifth ring (below) that I present is made of aluminum with inserted copper cubes and it contains a thought of Hector Berlioz that first appeared on the pages of Construction of Reality since at least a year and a half. It says:

A playful font (above), very extended and the most complex caustic shown thus far because the height of the light source is just above the ring. This kind of caustics is also called nephroid caustics because its root looks like a kidney.

Pick your favorite, I would take Nietzshe's or Satie's ring for myself.

Still, I like the most the playful caustic in the refracted light on the bottom of the sea shallow. A flickering network of light dances on pebbles and little fish. I could watch is for hours. And then jump in it. SPLAAAASHHHH !

Last updated on 21st of February 2018.