In this paper, we consider the optimal converter placement problem for a given number of converters on a path topology in an all-optical WDM networks. The placement of converters on a path divides the path into segments. A segment is defined as a set of links between two consecutive converters on a path. We first introduce and prove that optimal placement considering end-to-end performance is obtained when segments on a path have equal blocking probability. This result is then used to achieve optimal converter placement using both the link-load independence model and link-load correlation model. It is not always possible to divide a path into segments with equal blocking probability due to the arbitrary values of the load on each link. Three implementation algorithms that approximately achieve minimum blocking probability with linear complexity are then proposed. The algorithms can be readily extended to ring networks.