The Back-n white neutron source at the China Spallation Neutron Source (CSNS) provides neutrons in the continuous energy region from 0.5 eV to 200 MeV. A spectrometer named Light charged Particle Detector Array (LPDA) is designed for the study of (n, lcp) reactions at Back-n. The main detector of the LPDA spectrometer, a 16-unit ΔE-ΔE-E telescope array, is composed of two arrays of 8-unit ΔE-ΔE-E telescope. Each telescope unit consists of a Low-Pressure Multi-Wire Proportional Chamber (LPMWPC), a Si-PIN detector, and a CsI(Tl) scintillator detector. In 2021, a neutron-proton (n-p) scattering reaction cross-section measurement experiment was accomplished as the first experiment of the telescope array. Protons can be clearly identified in the ΔE-E spectrum (LPMWPC + Si-PIN) and the ΔE-E spectrum (Si-PIN + CsI(Tl)). Cross sections of the n-p scattering reaction in the neutron energy range of several MeV are extracted. The ΔE-E method also provides new measurement opportunities for many-body neutron induced light charged-particle emission reactions.