"Not sure what is meant by ' a carefully designed normal map applied.'"

I was explaining what the circumstances could be. If I had told you the only way to get the effect you described was a curved (not flat) mirror, then I would have told a lie. There are two ways to get the effect. A curved mirror is most likely, but it is possible to do this also with a perfectly flat mirror, if you have a way to alter the normals. A normal map (or bump map but these differ only in the assembly - they do the same thing) can distort the surface of an otherwise completely flat geometry.

Here is a demonstration - the square mirror is completely flat. I am sure because I made it. It is a single 4-sided polygon, with all four vertices in the same plane. The reflections are distorted by a carefully designed normal map. In particular, it is a parabolic normal map - it mimics the curvature of a parabolic mirror.

I'm in no way suggesting this is your situation. I included the possibility of altered normals to prevent the potential exhibition of pedantry that might have ensued if I'd made the inaccurate claim that the only possibility is a curved mirror.

Note: Your mirror geometry may indeed be flat, and the curve is being added because the edges are welded to other non-coplanar polygons and you enabled smoothing. Smoothing bends polygons into curves to make organic surfaces smooth. If you have smoothing on for the mirror, turn it off.

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Renderosity forum reply notifications are wonky. If I read a follow-up in a thread, but I don't myself reply, then notifications no longer happen AT ALL on that thread. So if I seem to be ignoring a question, that's why. (Updated September 23, 2019)