The next generation wide-field X-ray telescope (WFXT) will require an angular resolution of ~5-10 arcsec almost constant across a wide field of view (~1 deg2 diameter). To achieve this goal, the design of the optical system has to be based on mirrors characterized by short length and polynomial profiles, as well as focal plane curvature and plate scale corrections. These concepts guarantee an improved angular resolution at large off-axis angle with respect to the normally used Wolter-I configuration. These telescopes are therefore optimal for survey purposes. A significant increase of effective area and grasp with respect to previous missions must also be achieved. This is possible with high precision but at the same time thin (2-3 mm thickness for mirror diameters of 30-110 cm) glass mirror shells. To achieve the goal of 5 arcsec and improve further the technology, we are considering different materials. Fused silica, a well-known material with good thermo-mechanical and polishability characteristics provide the best choice. To bring the mirror shells to the needed accuracy, we are adopting a deterministic direct polishing method (already used for past missions as Einstein, Rosat, Chandra). The technological challenge now is to apply it for almost ten times thinner shells.