We are investigating the design and fabrication of multilayers of various materials to be used as reflectors in the extreme ultraviolet wavelength range. The reflectance versus angle of incidence (10° to 85° from normal) has been measured for a multilayer of silver and silicon at 58.4 nm. We have discovered that contamination layers on the surface of these multilayers can cause significant degradation in their performance. Optical constants for silver from two references were quite different at this wavelength and our measurements have resolved this discrepancy in favor of one of the published values. The absorption coefficient for silicon was found to be somewhat higher than the published value at 58.4 nm. These reflectors could be utilized as polarizing components at this wavelength if the angle of incidence is approximately 40°.