Multilayer-film mirrors are disclosed that exhibit high reflectivity to incident X-radiation independently of the angle of incidence and without significantly compromising optical performance. Also disclosed are X-ray optical systems and microlithography apparatus comprising such mirrors. In an embodiment a multilayer-film mirror is formed by alternately laminating Mo layers (a material in which the difference between its refractive index in the weak X-ray band and its refractive index in a vacuum is great) and Si layers (a material in which said difference is small) on a substrate. The ratio (null) of the thickness of the Mo layer to the total of the thickness of the Mo layer and the thickness of the Si layer has a distribution based on the distribution of angles of incidence of X-radiation on the mirror surface. By providing null with a distribution that corresponds with the distribution of the angles of incidence in the mirror surface, maximum reflectivity can be obtained at the angles of incidence at various points within the mirror surface. Because there is no need to change the period length in this case, there is no deterioration in the optical performance of the mirror.