“Who gave him the 'authority' to do this?” “He didn't do it 'on his own authority' [=he didn't do it on his own]; he was acting 'under the authority of' the company president.” [=the company president gave him the power to do it]
No one 'in authority' objected to the plan. = No one 'in a position of authority' objected to the plan. [=no one with official power to make important decisions objected to the plan]
This office has 'authority' over personnel matters. [=this office has the power to make decisions about personnel matters]
(..) - Alright. Stay calm, everybody! We're getting reports, there are total blackouts in the north and to the northwest of the city. Federal authorities are trying to determine if this is part of a larger terrorist attack. Ancient Kryptonian deformity. The blood of my blood. Born to destroy you. (..)2016 Batman v Superman: Dawn of Justice