This page in our guide to Control contains a solution to the puzzle with the mirror. This puzzle appears during Self-reflection side mission.
First, you need to get to the Sector: Research and go to Mirror Testing lab by getting there from the Ritual Division. There is a panel in the center of the room - you can look at two different reflections and determine how to open the door in the chamber with the mirror. The pictures above show the solution and the order of the doors.
Set all the windows in this way - the doors leading to the large mirror will be opened. Interact with the mirror and you will find yourself in an alternative mirror world. Inside, you will, e.g. fight esseJ.