The number of damped Ly-alpha absorbers (DLAs) currently known is about 100, but our knowledge of their sizes and morphologies is still very sparse as very few have been detected in emission. Here we present narrow-band and broad-band observations of a DLA in the field of the quasar pair Q0151+048A (qA) and Q0151+048B (qB). These two quasars have very similar redshifts z_em = 1.922, 1.937, respectively, and an angular separation of 3.27 arcsec. The spectrum of qA contains a DLA at z_abs = 1.9342 (close to the emission redshift) which shows an emission line in the trough, detected at 4 sigma. Our narrow-band image confirms this detection and we find Ly-alpha emission from an extended area covering 6x3 arcsec^2, corresponding to 25x12h^-2 kpc^2 (q0=0.5, H0 = 100h km s^-1). The total Ly-alpha luminosity from the DLA is 1.2 x 10^43 h^-2 erg s^-1, which is a factor of several higher than the Ly-alpha luminosity found from other DLAs. The narrow-band image also indicates that qB is not covered by the DLA. This fact, together with the large equivalent width of the emission line from the Ly-alpha cloud, the large luminosity, and the 300 km s^-1 blueshift relative to the DLA, can plausibly be explained if qB is the sourceof a Lyman-limit system. We also consider the relation between DLAs and Lyman-break galaxies (LBGs). If DLAs are gaseous disks surrounding LBGs, and if the apparent brightnesses and impact parameters of the few identified DLAs are representative of the brighter members of the population, then the luminosity distribution of DLAs is nearly flat, and we would expect that some 70% of the galaxy counterparts to DLAs at z=3 are fainter than m_R=28.
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