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You can adjust the height of the light source and those bulbs have a beam angle as narrow as 10°, usually around 40°, getting it glare-free seems trivial.
Mirrors, either glass or polished metal, work fairly well for reading lamps, see Castiglioni's Gibigiana.This one seems to use some sort of coated specialty glass.

https://vimeo.com/242368762
gertrudestein
Yes, or at least i think so. It looks like an LED MR16 lamp. Why the fuck you want to shine it at a mirror is beyond me. On the off chance you don't get direct glare as you walk anywhere near it you can rest assured when you sit down you'll have a bright light source reflected back in your face.