I recently made a physical object that defies all intuition. It's a square of acrylic, smooth on both sides, totally transparent. A tiny window.
Caustics are the bright patches of light we see when illuminating a transparent object. All the photons that don't pass through the object are what form the object's shadow. All those photons have to go somewhere; they contribute to the caustic pattern.
The most interesting aspect of caustics is that they arise from even the tiniest of variations in surface flatness. Even the gentlest waves on the surface of a pool form powerful lenses that cast intense caustics on the floor below.
The reason my acrylic square can project an image is because I've distributed just the right amount of concavity and convexity into the surface so that the refracted light forms a caustic image.
This lens forms the simplest possible caustic. If all the incoming light is from a single, very distant light source like the Sun, this lens focuses all of its incoming light into a single point. The caustic image from this lens is dark everywhere with one very bright spot in the center.