Why does ray tracing work (even if it is wrong?)
Imagine a super ray box, one, just as big, with not 5 but 500, or even 5000 beams? How would all those beams behave?
There is no reason why they should behave any differently than the main 5 we can see on
the video clip.
By the way, if you need a reliable image of the ray box and of the beams coming out of it, you will have to go further than the first point at which all 5 become distinguishable. You will have to wait until the spatial relationship of the elements of the image is proportional to that of the same elements in the object. In other words, just like in the object, the image will have to show 5 beams equally spaced from each other.
I wonder, and I must precise that I have not made the experiment yet, whether that image. with the beams equally spaced, will be there where ray tracing says it should be.
Let me know if you have the opportunity to do such an experiment.
Concerning the question in the title, I also have to admit that I am not really sure I've got the answer.
Consider the following as a first attempt.
Ray tracing is based on a fundamental assumption, that each point on the object reflects (or propagates) light in all directions, a physical impossibility which is then covered up by the even more slippery concept of wave.
As we can see each time we shine a light beam through a lens, this assumption is blatantly false.
We do not need to use laser beams, normal light going through splits would give the same results.
Back to our puzzle: how could ray tracing be so accurate if it is wrong?
My first reaction would be to say that it is geometrically accurate, even if empirically wrong. When tracing the ray from each point of the object -and let's take the perennial arrow as our model- each point of the arrow will be represented (ideally) by one point of the image, and all those points will be easily linked by a single line equivalent to that of the arrow.
What ray tracing does is, I think, start from this empirical situation and try and find a logical, geometrical explanation as to how all these points appear to be connected. And the assumption of each point reflecting multiple rays appears to be the perfect solution.
I would like to coin the expression "ad hoc rationality" to express a natural thinking process which consists in finding, or inventing, reasons that explain for us the behavior of not only objects and processes, but also of people.
The danger of such a procedure is that we can easily be tempted to stop looking at the empirical facts and only see what the theory tells us to see.
Such a danger is inevitable and should not be exaggerated, since there is no alternative for such a way of thinking.
Furthermore, mere rational and logical explanations meet sooner or later empirical obstacles they cannot explain away anymore.
I think such a simple video clip as the one presented above, can be such a wall.