Arrange a different change in what happens between the source and the detector, this time by arranging it so that the photons must change medium as they explore the space between the source and a detector: to explore refraction. Here you might guess that the significant paths will be those which have waypoints on the surface between the media. You'll want to vary the waypoints for a variety of source and detector positions to get a complete picture of how the illumination varies.
Again you're looking for triplets of paths where the contributions line up, giving a large resultant, and so predicting a brightness, or the opposite, where the triplets curl up, predicting darkness.
Careful exploration will recover the empirical laws of refraction, that only specific relative locations for the source, interface between the two media, and the detector result in an illuminated detector.(An elaboration of this model can predict
Snell's Law which is the quantitative empirical law of refraction. Physicists often get excited when they can account for an empirical law with a theoretical model, so now might be a good time to
take a moment.)
As an extension you might look deeper, inot the variation in trip time between paths, as its the trip time that sets the arrow rotation. Where the difference in trip time between adjacent paths is small, the contributions from those paths will line up.