Maximum physical size of H II regions ﹩{R}_{S}^{{\rm{\max }}}﹩ versus source redshift z_s for different BH masses (5, 10, and 20 M_⊙) and distances (0.1, 1, and 10 kpc), with the top x-axis showing the corresponding angular diameter distance D_S in Mpc. ﹩{R}_{S}^{{\rm{\max }}}﹩ defines the upper size limit of the H II region within which significant lensing magnification can be produced.