Feynman Lec, problem with diffraction

[rpf_rr]

Homework Statement

It is a thing feynman doesn't explain, it is meant to be obvious, but for me and some friends is not. If you have the first book, chapter 30-6, "Diffraction by opaque screen", he is talking about the approssimation of the two path: for finite distance is h^2/s, and is quadratic proportional to h, while if you go to infinity, that is the point, is linearly proportional to h. I really don't understand what does it means, the approssimation is more good if you go to infinity, is always quadratic, for any finite distance, the limit is proportional to h^2. It is an important sentence, for him this is the advantage of the "sources" method

Homework Equations

You have to read all the passages of the book, if you don't have it i can send that page to you.

The Attempt at a Solution

Another note, say that the difference of paths is linearly proportional to h is like saying that the path is equivalent (times a coefficient) to the path going straight on and then go 90 deg to the right, that for me is not the fastest

 

[NateD]

way, so it is not the most efficient. I think that the solution of this paradox is that we are talking about the limit of h going to infinity, so if we go to infinity, the difference between the two paths is always proportional to h, and the approssimation is more good.