The prospects for imaging X rays at energies from 10 to 40 keV with grazing incidence optics are explored. The scientific rationale and existing laboratory measurements are reviewed. Measurements of reflectivity using possible mirror materials are described. Iridium-coated float glass gives an improved performance over gold by the factor predicted by theory, but both had a lower absolute level. This may be due to a lower density of the thin metal layer caused by the deposition method. The reflectivity of a sample of iridium-coated float glass was measured at small grazing angles (25-5 min of arc) at energies of 8, 17, and 26 keV. High reflectivity (greater than 50 percent) was seen out to angles of 33, 16, and 11 min of arc, respectively. These are close to the theoretical values. A design for a high energy imaging telescope of the Explorer class is described.