A monocle was a type of glass lens used for only one eye.
The First Doctor used a monocle when he encountered the Sensorites, (TV: The Sensorites [+]Peter R. Newman, Doctor Who season 1 (BBC1, 1964).) Fomal, (PROSE: The Sons of the Crab [+]The Dr Who Annual 1966 (Doctor Who annual, 1965).) the Korads, (PROSE: Peril in Mechanistria [+]The Dr Who Annual 1966 (Doctor Who annual, 1965).) the Voord (PROSE: The Fishmen of Kandalinga [+]The Dr Who Annual 1966 (Doctor Who annual, 1965).) and the Testimony Foundation. (TV: Twice Upon a Time [+]Steven Moffat, Doctor Who Christmas Special 2017 (BBC One, 2017).) When visiting the Space Museum, he used it to inspect a piece of technology. (TV: "The Dimensions of Time" [+]Part of The Space Museum, Glyn Jones, Doctor Who season 2 (BBC1, 1965).) While in the ruins of Villengard, he used his monocle to examine a discarded eyestalk. (TV: Twice Upon a Time [+]Steven Moffat, Doctor Who Christmas Special 2017 (BBC One, 2017).)
A monocle was still in the pockets of the Second Doctor. (AUDIO: The Last Day at Work [+]Harry Draper, Short Trips (Big Finish Productions, 2018).)
The War Lord von Weich used a monocle to implant suggestions into the minds of his human subordinates. (TV: The War Games [+]Terrance Dicks and Malcolm Hulke, Doctor Who season 6 (BBC1, 1969).)
The Seventh Doctor wore a monocle as part of his Reichsinspektor General guise. (PROSE: Timewyrm: Exodus [+]Terrance Dicks, Virgin New Adventures (Virgin Books, 1991).)
Seth Rakoff wore a monocle. (COMIC: The Curse of the Scarab [+]Alan Barnes, DWM Comics (Marvel Comics UK, 1995).)
Major George Beresford wore a monocle. (AUDIO: The Charge of the Night Brigade [+]Error: Code 2 - no data stored in variables, cache or SMW.)
The computer Gus used the image of a monocle as its avatar. (TV: Mummy on the Orient Express [+]Jamie Mathieson, Doctor Who series 8 (BBC One, 2014).)
A monocle was one of the über-stereotypical traits of German antagonist Doctor Von Badguy II in a highly generic World War II film that was one of the features that Archimedes Von Ahnerabe's life had been processed into by Auteur. (PROSE: White Canvas [+]James Wylder, A 10,000 Dawns Christmas and The Outer Universe Collection (10,000 Dawns stories featuring DWU elements, Arcbeatle Press, 2018).)