We present Keck II NIRSPEC rest-frame optical spectra for three recently discovered lensed galaxies: the Cosmic Horseshoe (z = 2.38), the Clone (z = 2.00), and SDSS J090122.37+181432.3 (z = 2.26). The boost in signal-to-noise ratio (S/N) from gravitational lensing provides an unusually detailed view of the physical conditions in these objects. A full complement of high S/N rest-frame optical emission lines is measured, spanning from rest-frame 3600 to 6800AA, including robust detections of fainter lines such as H-gamma, [SII]6717,6732, and in one instance [NeII]3869. SDSS J090122.37+181432.3 shows evidence for AGN activity, and therefore we focus our analysis on star-forming regions in the Cosmic Horseshoe and the Clone. For these two objects, we estimate a wide range of physical properties, including star-formation rate (SFR), metallicity, dynamical mass, and dust extinction. In all respects, the lensed objects appear fairly typical of UV-selected star-forming galaxies at z~2. The Clone occupies a position on the emission-line diagnostic diagram of [OIII]/H-beta vs. [NII]/H-alpha that is offset from the locations of z~0 galaxies. Our new NIRSPEC measurements may provide quantitative insights into why high-redshift objects display such properties. From the [SII] line ratio, high electron densities (~1000 cm^(-3)) are inferred compared to local galaxies, and [OIII]/[OII] line ratios indicate higher ionization parameters compared to the local population. Building on previous similar results at z~2, these measurements provide further evidence (at high S/N) that star-forming regions are significantly different in high-redshift galaxies, compared to their local counterparts (abridged).
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