We present the optical design of GMOX, the Gemini Multi-Object eXtra-wide-band spectrograph. GMOX was selected as part of the Gemini Instrument Feasibility Study to develop capabilities and requirements for the next facility instrument (Gen4#3) for the observatory. We envision GMOX covering the entire optical/near-IR wavelength range accessible from the ground, from 3500 Å in the U band up to 2.4 μm in the K band, with nominal resolving power R≃5,000. To maximize efficiency, the bandpass is split into three spectrograph arms - blue, red, and near-infrared - with the near-infrared arm further split into three channels covering the Y+J, H, and K bands. At the heart of each arm is a Digital Micromirror Device (DMD) serving as a programmable slit array. This technology will enable GMOX to simultaneously acquire hundreds of spectra of faint sources in crowded fields with unparalleled spatial resolution, optimally adapting to both seeing-limited and diffraction limited conditions provided by ALTAIR and GeMS at Gemini North and South, respectively. Fed by GeMS at f/33, GMOX can synthesize slits as small as 40 mas (corresponding to a single HST/WFC3 CCD pixel) over its entire 85”x45” field of view. With either ALTAIR or the native telescope focal ratio of f/16, both the slit and field sizes double. In this paper we discuss the conceptual optical design of GMOX including, for each arm: the pre-slit optics, DMD slit array, off-axis Schmidt collimator, VPH grating, and refractive spectrograph and slit-viewing cameras.