In his popularized version of QED (Strange Theory...) Feynman explains reflection from an air-water boundary (including total internal reflection) by summing up the amplitudes of various paths that bend at the boundary but are straight everywhere else. As we add more contributions, we see a Cornu spiral that gives us a large amplitude for the actual classical path. (Fig. 29 in my edition). He does say this is a simplified picture, because it assumes straight lines that change direction only at the boundary. My question is, can we relax that assumption a little bit, and still get to the correct result? We don't want to go totally non-classical by considering arbitrarily curved paths, but we can include more various straight line paths with a single break / bend anywhere in the media. So let's consider a bundle of bent straight lines where some bend just below the boundary, and some bend above the boundary. So we're allowing the bending to happen anywhere within the media, and not necessarily at the boundary. If we sum these paths, will they add up correctly and work as if the bending was effectively at the boundary?