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Originally Posted by Slavakion
How would you burst into flames? That would imply that energy is being added to the system. From what you described, you have only made it so that energy does not become depleted by imperfections in the mirror(s).
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Light is being added to the system without end because the flashlight never runs out of battery power. That glowing piece of wire is adding energy to the system with every moment.
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Originally Posted by Slavakion
Is the light bouncing directly back and forth between two points, or randomly? That would make a difference, as with the former you would have to be in the path of the light in order to see it (I'm assuming the light isn't being reflected by air particles which would ruin the "perfect mirror" setup).
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The light is not bouncing back and forth between only two points, nor is it bouncing randomly. Since the diffuse light source is not in the exact center of the sphere you could get certain paths of light that go around the sphere for many revolutions before meeting a part of your body. I am not familiar with the visual output of a reflection of a person after being reflected billions of times from slanted concave mirrors, but I am guessing that by moving your head and catching paths of light you did not before would be very unlikely to yield a focused image.