NavList:

Frank you wrote:

The problem could be extended and the optical analogy continued by adding a marsh to the problem. Suppose there is marshy ground on either side of the river. On normal ground the farmer can walk at 4mph. On marshy ground the farmer can walk at 2mph. The change in speed is equivalent to refraction and shifts the fastest path towards the perpendicular to the river bank on the portions in the marsh.

Actually, it’s only marshy between late autumn and spring.  Funnily enough, in the winter he finds that if he heads a little bit further up river but cants right when he encounters the marsh so he ends up at the same point on the river that he aims for in the summer, he still has the easiest path, although it has to be admitted, the overall distance is slightly longer than in the summer.  Fortunately in this case, it’s still summer, so where does he aim for, and how far does he walk?  Being a 'rule of thumb sort of chap', he realises he can work out the distance very easily.  DaveP