After I replaced my car's left-side headlamp unit, which was cracked, the light beam on the left seems to be shorter than it was before. Did I buy the wrong headlamp unit? Or has it got something to do with the new bulb?
It is unlikely. The fact that you notice a short light beam from the new unit suggests that the lamp has not been correctly adjusted.
All headlamps can be adjusted for reach and spread or beam-length and beam- width respectively. Every car that leaves the factory has both lamps adjusted to the required specification.
Although adjustment is relatively simple - one screw for reach and one screw for spread - it is important to know the legal requirements of the beam stipulated mainly to avoid dazzling other road users.