An eye-mounted device includes a contact lens and an embedded imaging system. The front aperture of the imaging system faces away from the user's eye so that the image sensor in the imaging system detects imagery of a user's external environment. The optics for the imaging system has a folded optical path, which is advantageous for fitting the imaging system into the limited space within the contact lens. In one design, the optics for the imaging system is based on a two mirror design, with a concave mirror followed by a convex mirror.