Hot spots (HSs) are regions of enhanced radio emission produced by supersonic jets at the tip of the radio lobes of powerful radio sources. Obtained with the Very Large Telescope (VLT), images of the HSs in the radio galaxy 3C 445 show bright knots embedded in diffuse optical emission distributed along the post-shock region created by the impact of the jet into the intergalactic medium. The observations reported here confirm that relativistic electrons are accelerated by Fermi-I acceleration processes in HSs. Furthermore, both the diffuse emission tracing the rims of the front shock and the multiple knots demonstrate the presence of additional continuous re-acceleration processes of electrons (Fermi-II).