Derivation of Instrument Requirements for Polarimetry using Mg, Fe, and Mn lines between 250 and 290 nm

Judge et al. (2021) 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 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.