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I am a materials science undergraduate student. I have a question out of curiosity if it is possible to make a material that can completely make things invisible? What are the problems we will face in making it?
How can we achieve it?

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It has already been done by bending your view of the object. Basically you are looking beside the object instead of right at it. So what you see is the background that is beside/behind it. Take a look at Hyperstealth.net. This uses the same plastic as used for 3-D pictures you remember from years ago. I know the principals of this company.

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I'm not sure what your motivations are for making one (or maybe it's just curiosity!), but in principle, it should be possible. You must have the cloak partthat you can see (when it's not activated) emit the same radiation (when it's activated) that it receives on the side that you can't see (activated or not). The cloak must contain light sensors (which can sense the direction the light came from as well as the frequency of the light) and light emission units. Obviously, the sensors and emission units must communicate. In such a way that all received light, from whatever direction, is emitted on the other side. Maybe a small computer can take care of the right communication. The cloak will be somewhat heavy, but who knows in the future...

It can't be done by some special material on its own. There is no material that leads all incoming light in such a way that it looks as if the material wasn't there.

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