The second generation Low Resolution Spectrograph (LRS2) is a new facility instrument for the Hobby-Eberly Telescope (HET). Based on the design of the Visible Integral-field Replicable Unit Spectrograph (VIRUS), which is the new flagship instrument for carrying out the HET Dark Energy Experiment (HETDEX), LRS2 provides integral field spectroscopy for a seeing-limited field of 12 x 6 arcseconds. For LRS2, the replicable design of VIRUS has been leveraged to gain broad wavelength coverage from 370 nm to 1 micron, spread between two fiber-fed dual-channel spectrographs, each of which can operate as an independent instrument. The blue spectrograph, LRS2-B, covers 370-470 nm and 460-700 nm at fixed resolving powers of ~1900 and ~1100, respectively, while the red spectrograph, LRS2-R, covers 650-842 nm and 818-1050 nm with both of its channels having a resolving power of ~1800. In this paper, we present a detailed description of the instruments design in which we focus on the departures from the basic VIRUS framework. The primary modifications include the fore-optics that are used to feed the fiber integral field units at unity fill-factor, the cameras correcting optics and detectors, and the volume phase holographic grisms. We also present a model of the instruments sensitivity and a description of specific science cases that have driven the design of LRS2, including systematically studying the spatially resolved properties of extended Lyman-alpha blobs at 2 < z < 3. LRS2 will provide a powerful spectroscopic follow-up platform for large surveys such as HETDEX.
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