  Recently, we studied the magic wavelength for the atomic hydrogen 1S-2S
transition [A.K., Phys. Rev. A 92, 042507 (2015)]. An explicit summation over
virtual atomic states of the discrete part of the hydrogen spectrum was
performed to evaluate the atomic polarizability. In this paper, we supplement
the contribution of the continuum part of the spectrum and add the reduced-mass
correction. The magic wavelength, at which the lowest-order ac Stark shifts of
the 1S and 2S states are equal, is found to be equal to 514.6 nm. The ac Stark
shift at the magic wavelength is -221.6 Hz / (kW/cm^2), and the slope of the ac
Stark shift at the magic wavelength under a change of the driving laser
frequency is -0.2157 Hz/ (GHz kW/cm^2).
