Chromospheric LAyer Spectro-Polarimeter (CLASP2) was a sounding rocket experiment, which is a follow-up mission to the Chromospheric Lyman-Alpha Spectro-Polarimeter (CLASP1) in 2015. To measure the magnetic fields in the upper solar atmosphere in a highly quantitative manner, CLASP2 changes the target wavelengths from the hydrogen Ly-α line (121.567 nm) to Mg II lines near 280 nm. We reused the main structure and most of the optical components in the CLASP1 instrument, which reduced the turnaround time and cost. We added a magnifying optical system to maintain the wavelength resolution, even at the longer wavelength of CLASP2. Here, we describe the optical design and performance of the CLASP2 instrument.