This is the EVA wrist mirror flown on the Gemini XII mission in November 1966. Astronaut Buzz Aldrin successfully performed a two-hour long EVA completely outside the spacecraft, proving that with adequate hand-holds and other equipment, humans could work easily and efficiently in the vacuum of space. There is no evidence, however, including photographs, that show Aldrin using this mirror during either of his stand-up EVAs or the one spent entirely outside the spacecraft.
The Gemini program's purpose was to prepare astronauts and the engineers at NASA for the tasks required for the lunar landings of the Apollo program, so Aldrin's successful EVA on the final Gemini mission gave NASA confidence that their procedures for Apollo could be performed.
NASA transferred this mirror, with the Gemini XII spacecraft, to the Museum in 1968.
This object is not on display at the National Air and Space Museum. It is either on loan or in storage.