The stability of an injection-locked DFB 1.5 μm diode laser is studied systematically. A master diode laser with high spectral purity is used to injection lock a similar diode laser. The spectral purity of the master laser is successfully transmitted to the slave diode laser. A numerical simulation fits the experimental results and gives exact simple interpretations of the behavior of the slave diode laser. Three regimes occur at different injection levels. The relaxation hole appearing on the locking range pattern, for medium and strong injection regimes, is fully explained and leads to a complete explanation of the stability of the slave diode laser. As a consequence, two possible determinations of the Henry α factor [1] are presented, with a 5 % precision for one of them.