  The weak field approximation (WFA) is a conceptually simple and
computationally light method for inferring the magnetic field strength and its
orientation in the Sun's atmosphere. In this work we study the validity and
limitations of this tool when applied to full Stokes Ca II 8542 A profiles to
extract information about the chromospheric magnetic field. We find that the
range of validity of the WFA depends, amongst other things, on the component of
the magnetic field that one is trying to infer. The retrieval of line-of-sight
component of the chromospheric magnetic field from the core of the spectral
line is reliable for field strengths up to ~1200 G, even when moderate velocity
gradients are present. The horizontal component, on the other hand, is suitably
derived using the wing-core boundary of the spectral line, but typically yields
systematic errors of >10%. The effects of scattering polarization further
compound the problem by rendering the transverse field inference problematic in
quiet Sun areas, and for observing geometries within 30 degrees of the limb.
Magneto-optical effects disproportionately challenge the determination of the
magnetic field azimuth in the transverse plane, leading to errors of ~10
degrees. Typical noise levels of 10d-3 relative to the continuum intensity
preclude the accurate retrieval of the transverse field strength and its
azimuth below a threshold of a few hundred gauss. Striving for a noise level of
10d-4 significantly improves the diagnostic capability of the WFA with this
spectral line, at which point the magnetic field inference becomes limited by
systematic errors.
