When don't you need back coatings for plane mirrors?

If the angle of incidence is great enough, no reflective coating is needed on either the front or rear surface, because Total Internal Reflection takes place. See the related link for more details. Telescope mirror are coated with aluminum or silver on the front surface and not the back, to avoid refraction within the glass or other material, and to allow the optical qualities of the interior of the reflector support, to be much poorer than that of optical glass.