Restricted paths for propagation

Here is a situation where the paths are artificially restricted by two barriers. So the waypoints are restricted and you can investigate what effect this restriction has on the resultant of the contributions at different locations for the detector.

Use this array of resultants to predict the variation in brightness as you move the detector.

Here you have managed to predict diffraction using the same mechanism as you as accounted for reflection, refraction and propagation and so you should certainly take a moment to celebrate a bit of theoretical unifying but also demonstrate diffraction. The theory has shown you might expect to find something which you should then go out into the world and look for(an opportunity to exemplify a facet of reasoning in physics).

Restricted paths for reflection

The mirror was another situation where you've seen that the paths a long way from the obvious path did not contribute much. That is the meandering paths – those indirect paths explored by photons – did not result in contributions which made much difference to the overall brightness. Perhaps revisiting the mirror and restricting the paths might yield interesting results in the same way that restricting the paths did for propagation. Simply put, the ends of the mirror did not seem to make much difference, so let's start there.

Here are a triplet of paths with contributions that seem to curl up. Now restrict them in an interesting way, by removing the possibility of the central path. This results in an increase in the brightness as the contributions from the paths now tend to line-up rather than curl-up.

Less can mean more: fewer contributions result in more illumination. As stated at the beginning, it all depends on what's in the space explored between source and detector and how that stuff is arranged.

Systematically removing the possibility of every other path is done by creating lines where reflection is not possible – in other words a grating of lines. The model has now predicted the existence of diffraction gratings – so again take a moment to celebrate this once you have shown a diffraction grating in action.