This reflecting plate of polished steel was part of the equipment issued to John Glenn for his Friendship 7 mission in February, 1962, and was attached to his arm with the elastic band. As space was at a premium inside the Mercury spacecraft, the astronaut only had a very limited ability to move and see outside the craft. This plate behind his head and shoulders allowed the astronaut to see.
NASA - Manned Spacecraft Center transferred this to NASM in 1967.
This object is not on display at the National Air and Space Museum. It is either on loan or in storage.