The Son Of X-Shooter (SOXS)(1) is a medium resolution spectrograph (R similar to 4500) proposed for the ESO 3.6 m NTT. We present the optical design of the UV-VIS arm of SOXS which employs high efficiency ion-etched gratings used in first order (m = 1) as the main dispersers. The spectral band is split into four channels which are directed to individual gratings, and imaged simultaneously by a single three-element catadioptric camera. The expected throughput of our design is > 60% including contingency. The SOXS collaboration expects first light in early 2021. This paper is one of several papers presented in these proceedings(2-10) describing the full SOXS instrument.