if the sphere were perfectly round and the walls were highly reflective to visible light, what would happen
I don't see that it would hurtJust cut out a circular piece about 1 1/2 wide and set it on top of the outer edgeIf you're worried, just check it every few minutesNecessity-the mother of invention!
Assume the walls are coated with silver, you are tiny compared to the sphere, you are wearing a silver suit with a tiny peep hole, and the light bulb does not absorb any of the reflected lightRed light would be reflected back at the bulb about 5% dimmer each time until the reflections approach zero brightnessViolet would be about 10% dimmer each timeSo the total brightness for red inside the sphere would be the brightness of the bulb times Σ (n 0 to ∞)(.95^n) 20 times the original brightnessFor blue, Σ (n 0 to ∞)(.95^n) 10So the red would be amplified about twice as much as the violet(This is a good example of the usefulness of Wolframalpha.) For an aluminum coating, the reflectivity is about 92% for violet and 90% for red.
