  Refraction is a well-known optical phenomenon that alters the direction of
light waves propagating through matter. Microscopes, lenses and prisms based on
refraction are indispensable tools for controlling the properties of light
beams at visible, infrared, ultraviolet and X-ray wavelengths. The large
absorption of extreme-ultraviolet (XUV) radiation in matter, however, hinders
the development of refractive lenses and prisms in this spectral region. Here,
we demonstrate control over the refraction of XUV radiation by using a gas jet
with a density gradient across the XUV beam profile. A gas phase prism is
demonstrated that leads to a frequency-dependent deflection of the XUV beam.
The strong deflection in the vicinity of atomic resonances is further used to
develop a deformable XUV refractive lens, with low absorption and a focal
length that can be tuned by varying the gas pressure. Our results provide novel
opportunities in XUV science and open a route towards the transfer of
refraction-based techniques including microscopy and nanofocusing, which are
well established in other spectral regions, to the XUV domain.
