Suppose there were a great big hollow sphere made of looking-glass and you were sitting inside. Where would?

Question

it stop reflecting your face and begin reflecting your back?

Answer 1

By looking glass I assume you mean reflecting mirror.

There have been many long arguments over this one. It's been around for a long time.

You would see nothing unless there is a light. The light can't be at the center because you are there.

You can do ray tracing from the light to the mirror to your eyes to determine what you see.

Answer 2

It would look something like this, only warped:

http://dev.physicslab.org/Document.aspx?...

Depending on where you looked, you would see the front and back of your head, or one side and the other, but the image would be distored because of the curvature of the lens.  

By following the ray traces here you can see sort of what you would see by putting your head in the center and looking in a particular direction without moving your head.  

http://www.williamson-labs.com/images/mi...