I've looked at this a couple of times now, and to start, with the age of the box, I would say 20s or earlier. Plus the lack of stainless steel, or chrome, and painted metal and brass also points to some age. The clamp looks like it could be for attaching to a microscope. Mirrors were used before mini lamps were available to light specimens in microscopes, and this is a pretty large mirror for that use. With the lense that slips out of the way, one could align a slide, then bring the full focus part, the heavier magnification into play. So my guess is a rather unique early microscope attachment. Plus looking at the wear, it was used often, never sitting on the shelf too often.