late 14c., rarefien, "make thin, reduce the density of," from Old French rarefier (14c.) and directly from Medieval Latin rarificare, from Latin rarefacere "make thin, make rare," from rarus "rare, thin" (see rare (adj.1)) + facere "to make" (from PIE root *dhe- "to set, put"). Intransitive sense of "become less dense" is from 1650s. Related: Rarefied; rarefiable.
<a href="https://www.etymonline.com/word/rarify">Etymology of rarify by etymonline</a>
Harper, D. (n.d.). Etymology of rarify. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/rarify