NavList:

Frank: Reference your triangles drawing, I did something very similar (no pun intended) in my original investigations.  I didn’t report it, because I didn’t know which symbols Navlist would accept, and I didn’t want to start adding photos when the cute solution of a flip, a straight line, and a 345 was so pretty.  

I called the distance from the barn to the river a.  Then total distance = sqrt((2a)sqd + (8a/3)sqd) + sqrt(asqd + (4a/3)asqd) = sqrt(4asqd + 64asqd/9) + sqrt(asqd + 16asqd/9) = sqrt(100asqd/9) + sqrt(25asqd/9) = 10a/3 + 5a/3 = 15a/3 = 5a = 5 x 200 = 1000yds.

I’m not entirely sure experienced walkers would swallow your lens theory, because they all know to avoid marsh at all cost; stick to the firm ground despite the longer journey.  If crossing a marsh becomes inevitable, cross it at the narrowest possible point, probably at right angles, which rather defies any laws of refraction, but then it was only an example. DaveP