Sunday, 15 August 2010

A Thought Experiment

I have been pondering over this thought experiment for a few weeks.
Here is the experiment:

Imagine a perfectly spherical ball and imagine that the inside of the ball was a mirror. Imagine that you are standing inside this mirror ball with a portable light source such as a flashlight or a fluorescent light bulb (I'm trying to be green here!). You turn on the light source to illuminate the inside of the sphere. What would you see?

This thought experiment seems to have a deceptively simple solution as mirrors are something we are very familiar with. I started off with thinking about what would happen if we were in a cube in which the inner walls were were mirrors. Mirrors placed parallel to each other produce an infinite number of images. So I would see infinite copies of myself each successively smaller. But what of the lighting conditions? At first I thought that the room would be very bright. But after a bit of thought I realized that my surroundings would seem very dark indeed. I realized that I would be very brightly illuminated but the parallel universes on the other side of the mirror would be very dark except for my reflection.

Now how do I complete the analogy and carry the argument on to a perfectly spherical mirror? It is very difficult to develop an intuition for curved mirrors. In this case my best guess is that I would see infinite reflections of myself but the reflections would be distorted.

Now what if I turn off the light? This part of the solution is fun to figure out and alltogether less mysterious. The light that is inside the mirror would keep bouncing around until all the radiation is absorbed by my skin and clothes. So when I turn off the light I guess I would still see myself but as the radiation is absorbed I would slowly get dimmer and dimmer until all the radiation is absorbed.

But what if I just keep the light shining? In a ruby laser light bounces back and forth between two mirrors until it gets so intense that it escapes from one of the mirrors which is only partially silvered. So I think that would mean that if I kept the light shining I would slowly get brighter and brighter until the intensity of the radiation is so high that I will have to close my eyes to protect them from permanent damage.

All this is assuming that the mirrors are perfectly reflective. In reality no mirror is perfectly reflective and always absorbs some of the radiation.

Now this situation is very hypothetical and my reasoning may not be correct. So this post is open for comment and discussion. I would like to hear the opinions of others and have a discussion in the comments page. Maybe that will clear up some of the grey areas.
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