When two independently-prepared Bose-Einstein condensates are released from their corresponding traps, the absorption image of the overlapping clouds presents an interference pattern. Here we analyze a model introduced by Javanainen and Yoo (Phys. Rev. Lett. 76:161, 1996), who considered two atomic condensates described by plane waves propagating in opposite directions. We present an analytical argument for the measurement-induced breaking of the relative phase symmetry in this system, demonstrating how the phase gets localized after a large enough number of detection events.