In quantum optics, a two-level atom coupled to a single mode in an optical cavity is a well-studied subject. This setup has been described using well-known model Hamiltonians, such as the quantum Rabi model and the Jaynes-Cummings model. Since these two models are also widely used in recent investigations of polariton chemistry, here we briefly derive them from the truncated Pauli-Fierz Hamiltonian (Eq. 70). The original derivations of these two models are slightly different than the procedure outlined here, but the general physical insights are the same.