Efficient polarizing as well as non-polarizing mirrors for a wavelength of λ=121.6 nm (hydrogen Lyman-α radiation) are necessary to achieve an experimental determination of the magnetic field in the solar corona through the Hanle effect. We have designed, realized and characterized such mirrors. These consist of glass coated with a thin-film stack. The coatings use the most reflective (Al) and most transparent (fluorides) materials at this wavelength. Different coatings were explored which involve an increasing number of films in the coating stack. At the incident angle of maximum polarization where the p-polarized reflectivity R p is minimized, an s-polarized reflectivity R s as high as 69% is experimentally obtained with a coating made of a Fabry–Perot resonator. To our knowledge, this value is the highest ever reported for a polarizing mirror at this wavelength. Additionally, efficient non-polarizing mirrors have been designed and realized by using a two-layer coating (MgF2/Al/glass). By optimizing the fluoride layer thickness, a mirror with non-polarizing properties in the whole range of incident angles was realized.