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First I need to define my view of the starting situation:
You are floating in the middle of a 30 foot perfect sphere, the inside of which is a perfect mirror. There is nothing other than you and a flashlight in the sphere, not even air, but we are ignoring your requirements for life at the moment. You switch on the flashlight.
Now for what you would see:
The sphere is focused on one point, the center. If you were to look from that exact point then you would see your eye (or retina). However, because the light source is not in the exact center you will have more interesting things happen.
You would first probably see yourself, distorted by the curved surface. If you remained perfectly still then it would be a stable system as your body eventually would absorb all of the energy the flashlight was putting out (some paths of the light might be extremely long, and take some time to reach you). If you moved your head you might see interesting things, such as images of previous moments in the sphere that were still bouncing around, but most likely they would be smeared beyond recognition. After some time I think you would see an even glow of the average wavelength your body and clothing reflects and the color of the flashlight. If your flashlight did not ever run out of batteries, you would eventually burst into flame and your observations would end.
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