Welcome to the board, feel free to post/ask questions, folks are friendly here for the most part. Your shoot on Monday reminds me of my several shoots in a factory that manufactured industrial light fixtures. I had reflection in a glass dome of these lights and had to find a way to fix it. First of all the ambient light has to be eliminated. I had to have complete darkness in the warehouse except for my studio lights, even the windows had to be covered with cardboard to block the incoming daylight creating windows reflections in the domes. Make sure you position your studio light at such an angle that you don't catch their reflection. Another way I would attempt to solve your problem is to stretch a white fabric, a large diffuser screen might do it, aove the mirror in such an angle that only the white fabric will be reflected of the mirror into your camera. If you use a black backdrop behing the mirror and if you get the mirror to reflect the white fabric I think you will have a nice effect. Give yourself ample time to experiment with some of these variables that can affect your final outcome. Good luck
Mirrors are little tricky to work with, but can bring about interesting effects.

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