  We study the impact of the atmospheric differential chromatic refraction on
the measurements and precision of relative astrometry. Specifically, we address
the problem of measuring the separations of close pairs of binary stars with
adaptive optics in the J and K bands. We investigate the influence of weather
conditions, zenithal distance, star's spectral type and observing wavelength on
the astrometric precision and determine the accuracy of these parameters that
is necessary to detect exoplanets with existing and planned large ground based
telescopes with adaptive optics facilities.
  The analytical formulae for simple monochromatic refraction and a full
approach, as well as moderately simplified procedure, are used to compute
refraction corrections under a variety of observing conditions. It is shown
that the atmospheric refraction must be taken into account in astrometric
studies but the full procedure is not neccessary in many cases. Requirements
for achieving a certain astrometric precision are specified.
