Derivation of Instrument Requirements for Polarimetry Using Mg, Fe, and Mn Lines between 250 and 290 nm

Judge et al. recently argued that a region of the solar spectrum in the near-UV between about 250 and 290 nm is optimal for studying magnetism in the solar chromosphere, due to an abundance of Mg ii, Fe ii, and Fe i lines that sample various heights in the solar atmosphere. In this paper, we derive requirements for spectropolarimetric instruments to observe these lines. We derive a relationship between the desired sensitivity to magnetic field and the signal-to-noise ratio of the measurement from the weak-field approximation of the Zeeman effect. We find that many lines will exhibit observable polarization signals for both longitudinal and transverse magnetic field with reasonable amplitudes.