An optical system includes a lens assembly fixed to a base for projecting an image light onto a surface; a DMD assembly movably disposed at one side of the lens assembly for reflecting the light irradiated from a light source onto the lens assembly; supporting members disposed at the one side of the lens assembly for supporting the DMD assembly; and an adjuster for moving the DMD assembly to adjust a tilt. The adjuster includes a guide member having a screw hole and fixed to the base; an adjusting screw driven into the screw hole for moving the DMD assembly along a lengthwise direction of the guide member; and a push rod having an end connected to the DMD assembly and another end connected to the adjusting screw. The DMD assembly is movable by adjusting the adjusting screw so that a tilt angle can be easily and precisely adjusted.