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In fiction, a cloak that conveys invisibility to the wearer. In Harry Potter and the Philosopher's Stone Harry's first Christmas at Hogwarts is the first time he ever gets real presents, and one of these is something "fluid and silvery-grey" that lies in gleaming folds: "It was strange to the touch, like water woven into material." Ron recognises it and in awe tells him what it is and that it's extremely rare and valuable. Using this and the Marauder's Map their adventures include sneaking out to the nearby village at night. Harry doesn't know who gave it to him, since the note with it says
Your father left this in my possession before he died. It is time it was returned to you. Use it well.
A Very Merry Christmas to you.
Another fictional example is the Elven cloaks given to the Fellowship in Lórien, in The Lord of the Rings. These are not magic as the Elves would call it, and do not convey outright invisibility, but are marvellously effective camouflage, and very light.

A real invisibility cloak, of sorts, has been invented. Professor Susumu Tachi showed it off in May 2004 at NextFest, a technology conference in San Francisco organised by the magazine Wired.

Essentially, cameras on one side take pictures of the scene, and this is projected onto the other side, so that you see what you would see if the thing wasn't there.

The mechanism can in principle be applied to making anything "invisible", or more accurately transparent in one or both directions, such as solid parts of cars, planes, or walls, but the breakthrough was applying it to something as flexible as a cloak. It uses electronic beads to create a material the inventors call retro-reflectum, which you can easily imagine Harry or Hermione shouting out as a spell, but that's what they called it.

Professor Tachi first thought about the technique in 1977, but says early efforts looked flat and unrealistic when they were merely projecting onto a screen.

The University of Tokyo call it Optical Camouflage, rather more soberly, and its potential military applications are discussed on E2 under adaptive camouflage (before it had become a reality), and James Bond had it on his car in Die Another Day. The University call their technique Retro-reflective Projection Technology, and it was chosen by Time magazine as one of the coolest inventions of 2003.

I'm not sure that invisibility is the right word at all: camouflage, yes, in the sense that zebras and army lorries are both well camouflaged and easily visible. Pictures of it deployed tend to show things that look like visible objects with the scenes behind them showing through them to some degree.