A curved mirror can also focus. Displaced the waypoints at the end of this mirror so that the contributions from all the waypoints all line up. Then you will have predicted or even designed a focusing mirror.
The photon is perhaps the simplest example of a quantum object. It's therefore a good introduction to the quantum world – every aspect of the discussion here applies also to particles such as electrons, protons and neutrons. The world appears as a quantum place and this way of calculating what will happen is universal. It's the best model of the universe at a very small scale. It's certainly counterintuitive, but that's the way the world is. Physics has often progressed by encouraging us to think that things are not as they first seem and that our common sense may not be as reliable as we imagined(think Aristotle, think Newton, think Copernicus, think Einstein, amongst others).