The gravitational potential of clusters of galaxies acts as a cosmic telescope allowing us to find and study galaxies at fainter limits than otherwise possible and thus probe closer to the epoch of formation of the first galaxies. We use the Bullet Cluster 1E0657-56 (z = 0.296) as a case study, because its high mass and merging configuration makes it one of the most efficient cosmic telescopes we know. We develop a new algorithm to reconstruct the gravitational potential of the Bullet Cluster, based on a non-uniform adaptive grid, combining strong and weak gravitational lensing data derived from deep HST/ACS F606W-F775W-F850LP and ground-based imaging. We exploit this improved mass map to study z~5-6 Lyman Break Galaxies (LBGs), which we detect as dropouts. One of the LBGs is multiply imaged, providing a geometric confirmation of its high redshift, and is used to further improve our mass model. We quantify the uncertainties in the magnification map reconstruction in the intrinsic source luminosity, and in the volume surveyed, and show that they are negligible compared to sample variance when determining the luminosity function of high-redshift galaxies. With shallower and comparable magnitude limits to HUDF and GOODS, the Bullet cluster observations, after correcting for magnification, probe deeper into the luminosity function of the high redshift galaxies than GOODS and only slightly shallower than HUDF. We conclude that accurately focused cosmic telescopes are the most efficient way to sample the bright end of the luminosity function of high redshift galaxies and - in case they are multiply imaged - confirm their redshifts.
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