Multi-wavelength, optical to IR/sub-mm observations of 5 strongly lensed galaxies identified by the Herschel Lensing Survey, plus two well-studied lensed galaxies, MS1512-cB58 and the Cosmic Eye, for which we also provide updated Herschel measurements, are used to determine the physical properties of z~1.5-3 star-forming galaxies close to or below the detection limits of blank fields. We constrain their stellar and dust content, determine star formation rates and histories, dust attenuation and extinction laws, and other related properties. We perform SED-fits of the full photometry of each object as well for the optical and infrared parts separately, exploring various parameters, including nebular emission. The IR observations and emission line measurements, where available, are used a posteriori constraints on the models. Besides the various stellar population models we explore, we use the observed IR/UV ratio to estimate the extinction and create energy conserving models, that constrain most accurately the physical properties of our sources. Our sample has a median lensing-corrected IR luminosity ~ 3e11 Lsun, stellar masses between 2e9 and 2e11 Msun, and IR/UV luminosity ratios spanning a wide range. The dust masses of our galaxies are in the range 2 to 17e7 Msun, extending previous studies at the same redshift down to lower masses. We do not find any particular trend of the dust temperature Tdust with IR luminosity, suggesting an overall warmer dust regime at our redshift regardless of luminosity. Lensing enables us to study the detailed physical properties of individual IR-detected z~1.5-3 galaxies up to a factor ~10 fainter than achieved with deep blank field observations. We demonstrate that multi-wavelength observations combining stellar and dust emission can constrain star formation histories and extinction laws of star-forming galaxies.
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