Experimental spectroscopic studies are presented, in a 5.5-25.5 nm extreme-ultraviolet (EUV) wavelength range, of the light emitted from plasma produced by the irradiation of tin microdroplets by 5-ns-pulsed, 2-mu m-wavelength laser light. Emission spectra are compared to those obtained from plasma driven by 1-mu m-wavelength laser light over a range of laser intensities spanning approximately (0.3-5) x 10(11) W/cm(2), under otherwise identical conditions. Over this range of drive laser intensities, we find that similar spectra and underlying plasma charge state distributions are obtained when keeping the ratio of 1- to 2-mu m laser intensities fixed at a value of 2.1(6), which is in good agreement with RALEF-2D radiation-hydrodynamic simulations. Our experimental findings, supported by the simulations, indicate an approximately inversely proportional scaling similar to lambda(-1) of the relevant plasma electron density, and of the aforementioned required drive laser intensities, with drive laser wavelength lambda. This scaling also extends to the optical depth that is captured in the observed changes in spectra over a range of droplet diameters spanning 16-51 mu m at a constant laser intensity that maximizes the emission in a 2% bandwidth around 13.5 nm relative to the total spectral energy, the bandwidth relevant for EUV lithography. The significant improvement of the spectral performance of the 2-mu m- versus 1-mu m driven plasma provides strong motivation for the development of high-power, high-energy near-infrared lasers to enable the development of more efficient and powerful sources of EUV light.