Ok, this was killing me. I cheated.
I made a sphere with a reflective inside with OpenGL and put the camera in the center. At first I didn't see anything, so I put a square in the center of the sphere (the camera doesn't physically exist). So the square represents the person. I then made a light source emminate in the angle the camera was looking.
I saw just the reflection of the illuminated side of the square. If I reversed the direction of the light (have it point in the antipode of the camera's angle), then I saw a shadow of the square. It looked just like a solar eclipse, only.. with a square.
So, sorry, I cheated.
I'll try to post pics once I get a host. I need to write a screen-capture thingie first though. Window's print screen isn't latching onto the window I made. Writing screen-capture code will take longer than the sphere demo. I don't have the time for it right now because of midterms. I'll get back to you guys in a few days.
Of course, this isn't the real world so lets look at a few things:
Manx: Brown wouldn't be the color. Light doesn't refract when it's reflected, so it can't be split into a specific part of the visible spectrum.
Prosequence: Light can't continue infinately in the sphere because light cannot cover an infinite distance. Certainly light can cover a VERY long distance, but not with flashlights. From the origin of the flashlight to the edge of the sphere, the light will travel 15'. With every reflection after that the light will travel a maximum of 30'. Even less because that is the distance from the centerpoint... which is blocked by the person.
sen_tom: This is what the effect looks like. Nothing special unfortunatly