An optical element (14) transparent for radiation with a wavelength λ in the ultraviolet wavelength range below 250 nm, in particular at 193 nm, comprises a substrate (17) with a refractive index nS larger than 1.6, and an antireflection coating (16) formed on at least part of the surface of the substrate (17) between the substrate (17) and an ambient medium with a refractive index nA, preferably with nA=1.0. The antireflection coating (16) consists of a single layer of a material with a refractive index nL of about nL=√{square root over (nAnS)}, in particular nL>1.3, and the optical thickness dL of the single layer is about λ/4. The optical element (14) is preferably part of a projection objective (5) in a microlithography projection exposure apparatus (1) and located adjacent to a light-sensitive substrate (10).