'If the distance between the atom and the mirror is very small, it is physically impossible to distinguish between these two paths..'' The particle and its mirror image cannot be clearly separated any more. The atom moves towards the mirror and away from the mirror at the same time.
This may sound paradoxical and it is certainly impossible in classical phyiscs for macroscopic objects, but in quantum physics, such superpositions are a well-known phenomenon. ''This uncertainty about the state of the atom does not mean that the measurement lacks precision...It is a fundamental property of quantum physics: The particle is in both of the two possible states simultaneousely, it is in a superposition.''
...Observing interference it can be directly shown that the atom has indeed been traveling both paths at once.