We report on self-injection locking in InGaN/GaN (blue/green) and InGaP/AlGaInP (red) visible-light laser diodes. The free-space optical feedback path was accomplished via an external mirror. The effect of injection current, optical power injection ratio, and external cavity length on the spectral linewidth and modulation bandwidth of the lasers are investigated. Our results show that the laser performance was substantially improved. In particular, we achieved a significant increase of ~57% (1.53 GHz - 2.41 GHz) and ~ 31 % (1.72 GHz - 2.26 GHz) in the modulation bandwidth, and ~9 (1.0 nm to 0.11 nm) and ~ 9 (0.63 nm to 0.07nm) times reduction in spectral linewidth of the green and blue lasers, respectively. Consequently, side-mode-suppression-ratio was considerably increased in all the cases, reaching as high as ~20 dB in self-injection locked blue laser diode, thus enabling a close to single mode operation. This work paves the way for attaining high speed optical wireless communications by overcoming the challenges of limited modulation bandwidth and multimode operation of visible laser diodes with this simple scheme.