We show that the recently discovered optical and ultraviolet light from the X-ray burst source 4U 1820-30 in the globular cluster NGC 6624 is due to reprocessing of the X-rays in the outer regions of an optically thick, geometrically thin accretion disk. We suggest that observation of orbital modulation of the reprocessed light, due to the variable contribution made as the heated face of the companion turns toward and away from the observer, would provide constraints on the inclination of the binary orbit, and we suggest that detection in the reprocessed flux of the '' red noise '' already observed in the X-rays would provide useful constraints on the geometry and physics of the accretion disk.