  Numerical integration of the differential equations of light propagation in
the Schwarzschild metric shows that in some extreme situations relevant for
practical observations (e.g. for Gaia) the well-known standard post-Newtonian
formula for the boundary problem has an error up to 16 \muas. The aim of this
note is to identify the reason for this error and to derive an extended formula
accurate at the level of 1 \muas as needed e.g. for Gaia.
  The analytical parametrized post-post-Newtonian solution for light
propagation derived by \citet{report1} gives the solution for the boundary
problem with all analytical terms of order $\OO4$ taken into account. Giving an
analytical upper estimates of each term we investigate which
post-post-Newtonian terms may play a role for an observer in the solar system
at the level of 1 \muas. We conclude that only one post-post-Newtonian term
remains important for this numerical accuracy and derive a simplified
analytical solution for the boundary problem for light propagation containing
all the terms that are indeed relevant at the level of 1 \muas. The derived
analytical solution has been verified using the results of a high-accuracy
numerical integration of differential equations of light propagation and found
to be correct at the level well below 1 \muas for arbitrary observer situated
within the solar system.
