Why can't you use fiber optics to make a cloaking device?

Won't work on several levels.

First, your eye has a resolution of about a million pixels, so just to mask in one direction, you would need a million cables.

Second, that only works in that direction. Walk around the object by 90 degrees where you see the cables from the side, and the illusion is lost. In fact, move just a little and the illusion is lost, as you should see a different background, but you see the same one.

Third, the cables have to bow out to get around the object, and the sides would be visible where they bow out.

fourth, the transmission of light is not perfect, so the background would be dim and noticeable.

sixth, the pattern of the image from the cables would be noticeable. You would see artifacts.

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In effect, you mean placing an image in front of it. Why bother when you can hang a picture in front of it?

There's a guy at UCB who has managed to create a cloak using I believe nanoparticles or nano-mirrors to mask small objects (very small). Theoretically you need to bend light around an object and the amount of gravity needed to do that is immense.