Huygens revisited (3)
Let me first mention a serious flaw also in my own analysis, one which I already mentioned in passing and which no other theory can explain either.
I have no idea how to explain that objects reflect their image only upside down, except in a mirror. More precisely, why only upside down images appear in pinhole darkrooms and on photo negatives (and none in mirrors)?
It would seem to me that there where an upside image is possible, a normal one should be also. How come we do not see that? What are we all missing?
You can build a very simple diagram with a program like Paint. 
First you need a vertical line somewhere in the middle of the screen, with a slit in it. Then draw a triangle with its top up on the left side, preferably not in front of the slit.
You can now draw two sets of lines. The first set is parallel and shows a simple translation of the triangle from one side to the other. The upper line will pass close to the upper part of the slit, and the lower line to the lower part. At the end we will have an identical image of the object.
The second set will show the familiar drawing of crossing rays creating an upside down image on the other side.
What is important is that both images are possible.
Of course, when using a converging lens only the second, classical, case will be possible, but what about a naked pinhole?
There does not seem to be any rational solution to this puzzle, only strange ones like all rays emitted by an object somehow have to say together, or some other mystical explanation.

Until we change the given of the problem. Both models assume that the image of the object nicely aligns its rays in such a way that they cross the slit in the same or exactly in the inverse order, top to top (or bottom) and bottom to bottom (or top). Such a view gives us indeed only two solutions, a translation or an inversion, and we are back to our dilemma.
It becomes very different when we make all points of the object pass either close to the upper or, alternatively, the lower side of the slit. Then, even if all lines seem to cross at the same point, they all end up at a different location, in an inverse order.
Apparently, just like by the use of a lens, rays cross each other and swap positions, only the location of the crossing is different. This would also explain why a small hole gives sharper images than a larger one.

But doesn't that mean that light does have a direction? Absolutely, we can simply direct our flashlight to wherever we want. In this sense, the beam has a direction. That does not mean that individual particles also do, except as part of the beam. Here again we can consider the light shining in space as a grid of stationary particles.

One thing this analysis still does not explain yet, is where the other images have disappeared. I surmise it will have something to do with focal length, and the relative distance of all the factors involved. I will just have to admit my ignorance even while expressing my conviction that rational, and empirically supported, explanations can be found.

Ray Optics revisited
I would like to present an alternative explanation of what happens when rays go through a converging lens. It consists in considering the crossing point as a slit, which would explain why in both cases the image is reversed. Ray optics describes this point mathematically, as an abstract point, which we know is empirically untenable. By considering it as a slit we can more easily look for empirical explanations as to what is happening in this portion of space.