Theater technical question: can you set up a mirror on stage that looks like an ordinary looking glass one minute, then change the lighting and suddenly it’s transparent?
I know about the so-called “Pepper’s Ghost” effect. That isn’t what I mean.
Imagine a woman looking at her reflection in a mirror, when her reflection dissolves away and there’s someone else looking out of the glass. Can it be done?
Two way mirror or a refelctive tinting and the appropriate lighting and it should be fairly easy.
ETA, find a building that has shiney reflective windows (they kind where you see the reflection of the sky on the side of the building). Now drive by it at night and you’ll be able to see the people in the offices.
Yes, if you put someone in a dark box with a half-silvered mirrored front, you can do what you want. Turning on bright lights inside the box, and lowering the external lights will cause the person in the box to become visible.
I figured it could be done — that’s pretty much as I suspected. Half-silvered glass, eh? 
It’s just a one-way mirror, the same as the ones they use on police procedurals and in day care classrooms.
Isn’t this the Phantom of the Opera trick? Not only do we see Christine’s reflection, but once it goes clear, we see the Phantom behind the “glass”, and then the actor’s arm comes through it and the actress follows him to the other side. Obviously, at some point in there, they get rid of the glass, but it most definitely acts as a mirror first. Productions I’ve seen have included glimpses of the orchestra in the mirror, so it’s not the identically costumed double on the other side of a picture frame trick.
Yup. A light is slowly turned on behind the mirror illuminating the Phantom’s face & making it visible behind the mirror.
Hang on, folks. Note exactly what the OP asks:
Bolding mine.
All the replies so far have described a method for getting the other image to appear on top of the first. But to make the first “dissolve away” and be replaced by the second will call for some careful lighting control. I’m not saying it’s impossible, but you’ll have to throw the first person’s face into (nearly) complete darkness to have the second person’s face replace it, as opposed to being superimposed on top of it.
But the more difficult issue has to do with sightlines. I think it would be nearly impossible for the replacement “reflection” to appear in the same place as the “real” reflection for every viewing angle in an ordinary theater. You could easily make it work on film, but in the theater it will be most effective only for a narrow range of seats.
Then there’s the problem of the mirror reflecting things you don’t want the audience to see: lighting instruments, the back side of the proscenium, the offstage wings, etc. It’s hard to use mirrors on stage.
Depending on exactly what you want accomplish, and given the sophistication of computer technology these days, it might be more effective to do this electronically: an HD monitor in a mirror frame and live or recorded visual effects.
What’s our budget for this effect? 
Maybe you could use a mirrored corner to reverse the person behind the one-way mirror?
Normally the back would dark and the front light to see the refelction, then slowly change reverse them. But like you said that would cause superimposing. What if the back was light, and the front was lighter, so as the front lights fade, the back is already bright enough for the crowd to see. I think this would make the reflection fade out, instead of the reflection fade out and the person behind fade in.
You could angle the mirror down a bit, that would help, giving it a convex shape would help a bit more. But I would think a small playhouse would be better suited for a trick like this.
I don’t know jack about technical theater, but I would think the easiest way would be one of two things, either a curtain that would allow an image to be projected from behind, and the the main character would just face the curtain and their reflection, the other person and the mirror itself would be prerecorded and projected onto the curtain, or I forgot my other idea. Eitherway, once you go pre-recorded you can figure out all the optical tricks in post processing.
Stage manager here.
I think a few of these responses are overcomplicating things. What you describe is a very simple effect, and the usual solution was hit upon immediately by Joey.
Have a one-way mirror set up tilted so that, for the majority of the audience, it reflects the auditorium ceiling. The tilt will not be noticible if the actress (Christine Daae, usually) stands close to the mirror. The front-lighting doesn’t even need to be especially strong as long as the back is completely dark.
Pish posh. The audience will see what it wants to see.
I just saw Phantom in Vegas, and they added some fog so that the glass dropping out of its frame couldn’t be seen. And their mirror was slightly trapezoidal to disguise the tilt.
Well, the theater I’m thinking of is 3/4 thrust, so it wouldn’t be effective for much of the house unless the mirror were placed as far upstage as possible — or unless instead of an actor behind the mirror, we had a flat image, like a cyc with the image projected onto it.