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We give an estimate of the relative error in the angular measurement ofobservations for high redshift objects induced by gravitational scatterings(lensing). Gunn (1967) concluded that the gravitational scatterings by galaxiesinduce the relative error of a few percent in the observations for objects at$z=1$. This estimate has been considered as a fundamental limitation ofaccuracy of the angular measurements in the observational cosmology. Inmultiple graviational scatterings, bending angle of single ray grows throughthe random work process. Gunn (1967) assumed that the difference of nearby raysalso grows through the random walk process. However, distance between nearbyphotons grows exponentially because the two rays suffer coherent scatterings bythe same scattering object. This exponential growth continues as long as thescattering is coherent. In the case of scattering by individual galaxies, theexponential growth continues until the angular distance reaches an arcminute orso. The relative error of the angular measurements under an arcminute due tothe exponential growth is $\sim 30\%$ at $z=1$ and exceeds $100\%$ at $z=3$, inthe case that the density parameter of galaxies is 0.2. The effects of clustersof galaxies or superclusters are more difficult to estimate accurately, butmight be significant. In the case of supercluster the angular measurements upto a few degrees could be affected.Comment: compressed uuencoded postscript, 8 pages including 5 figures, APJL  accepte

Exponential growth of distance between nearby rays due to multiple gravitational scatterings