The complex-valued index of refraction of germanium in the extreme ultraviolet (XUV) is measured by multi-angle reflectance of synchrotron radiation. The resulting index of refraction is higher resolution than previously measured values. It reveals new structures attributed to transitions from the 3d-core orbitals to the Σ𝑐5,2 and the 𝑋𝑐5,2 conduction bands. Additionally, it is shown that the problem of total external reflection, which renders multi-angle reflectance measurements insensitive to the complex-valued refractive index at grazing incidence, can be overcome by employing measurements at angles of incidence away from the critical angle.
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