A mirror doesn't add floor. It adds a picture of floor. Two simple facts explain almost everything it can do for a small room. First, light bounces off a mirror at the same angle it arrived at, like a ball off a wall. Second, a reflection appears as far behind the glass as the object is in front of it. Stand a lamp 1 m from a mirror and its reflection looks 1 m deep inside the wall.
So a mirror on the far wall of a 4 m room makes the room read as roughly 8 m long, as long as the mirror is big enough to show most of it and there is something worth looking at in the reflection. That is the illusion of space. The second effect is light: a mirror can carry daylight from a window to a corner that rarely gets any.
Below is a top-down plan of a 4 × 3 m room with a window in the top wall. Choose which wall the mirror goes on, drag it (or use the slider), and change where the light is coming from. Each line is a ray of light from the window.
Put the mirror on a side wall close to the window and the light that would have landed on one patch of wall gets thrown across the room instead. Put it directly opposite the window with the light coming straight in, and most of the beam goes back where it came from. In real life that second position is still good, because you see the sky or trees in the glass and the room feels like it has a second window. It just adds less actual brightness.
Now switch on the second room. The mirror makes your eye believe the space carries on behind the wall. The bigger the mirror, the more of that second room you see, which is why one large mirror usually does more than several small ones.
Place it where it will reflect something you like: a window, a lamp, a plant, a shelf you have tidied. A mirror facing a pile of laundry doubles the pile. At night a mirror beside a warm lamp makes that lamp look like two, which is a cheap way to make a room feel softer.
Next to a window and across from a window are the two classic spots. A hallway or a narrow room benefits most from a mirror on the long wall. In a very small, very dark room with no window, a mirror cannot make light, it can only reflect what is already there, so a lamp will help more.
Before you buy or move a big mirror, measure the wall width and the height from the floor to where the top edge would sit. Also measure the doorways, hallway turns and stairs it must travel through: large mirrors are heavy and awkward. If it will lean rather than hang, a tilted floor mirror needs a firm spot and, in a home with children or pets, a strap or fixing to stop it tipping.
For hanging, use fixings rated well above the mirror's weight and suited to your wall type, ideally into studs or with proper wall anchors. Think about what sits underneath: over a bed or sofa, use a secure fixing or choose another wall. In a rental, check your lease before drilling; a large mirror leaning on a sideboard or the floor works well and leaves no holes.
One safety note: curved or magnifying mirrors can focus sunlight into a hot spot. Keep those out of direct sun and away from curtains and paper.
You may already own the mirror you need: a hallway or bathroom mirror often works better on a living room wall. Second-hand shops, charity shops and online marketplaces are full of good mirrors with solid frames, usually for far less than new. Look at the glass in daylight before you commit; dark spots or cloudy edges mean the silvering behind it is wearing out. A mirror that is a little old and mismatched looks more like a home than a new one anyway.