We compute the two-point angular correlation function w ( \theta ) for a sample of \sim 1700 galaxies to a magnitude-limit equivalent to R~ { } \sim~ { } 29.5 using a catalog derived from the Hubble Deep Field images .
A non zero value of w ( \theta ) is measured down to R = 29.0 .
The amplitude of w ( \theta ) at the bright magnitude limit ( R~ { } \sim~ { } 26 ) is consistent with previous ground-based observations .
At fainter magnitudes the clustering amplitude continues to decrease but at a slower rate than that predicted by the power law w ( 1 ^ { \prime \prime } ) \propto 10 ^ { -0.27 R } observed for shallower samples .
The observed w ( \theta ) over the magnitude range 20 < R < 29 is consistent with linear evolution of the clustering of a galaxy population which at present has a correlation length r _ { 0 } of about 4 h ^ { -1 } Mpc , close to that of local IRAS galaxies .
We also investigate the impact that magnification bias induced by weak gravitational lensing may have on our results .
Although the observed amplitude of w ( \theta ) can differ from the true amplitude by up to 30 % , this effect is not large enough to affect our conclusions .
Finally , by using a color-selected sample , we examine whether the expected effects of magnification bias can be used for an independent determination of cosmological parameters in deep images .
We conclude that the amplitude of the effect can be large and in some cases even produce an upturn of the amplitude of the correlation with limiting magnitude .
However , we find that it is not possible to detect the effects of magnification bias on w ( \theta ) from images alone .
If redshift information becomes available , it is possible to measure the effects of magnification bias directly and thus constrain the density parameter \Omega _ { 0 } and the bias factor b .