A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2019 Nov 26, 08:57 -0800
Here's a crude illustration (image below) of the case with a marsh along the riverbank.
By the way, I have never encountered this farmer-river-barn problem before, but I strongly suspect that it was created and designed to invoke the optical analogy. There are, of course, multiple constructions for proving that the reflected path is the right one, and one could pull out any of these to avoid mentioning light rays if desired, but they're implicitly present in the construction of the puzzle.
Is there any connection to modern navigation? Obviously you can apply this directly to cases involving light reflecting off mirrors, for example in sextants. A more interesting application would be in "risk routing". If you need to transport a cargo but certain regions have moderately higher risk, then you can minimize total risk using this sort of optical analogy. The path of least risk would be refracted by zones of higher risk.