internally spherical mirror

Silenceisbliss

Say if one was to create a sphere whos inside surface was a perfectly dimensioned and flawless mirror.

so imagine a football whos internal walls are flawless and perfectly reflective.

Introduce a light source to the inside, and the photons will start bouncing around continuosly....right? (never mind the source of the light source and that it will absorb the light...just focus on the theory)

will this increase the temperature inside the sphere with all this mass bouncing around at the speed of light? or will it increase the pressure inside?

if you take said cylinder into a perfectly dark room and smash it, will you see a flash of the light?

Professor_Fink

Silenceisbliss wrote: »

Introduce a light source to the inside, and the photons will start bouncing around continuosly....right? (never mind the source of the light source and that it will absorb the light...just focus on the theory)

Obviously you can never actually build such a device, because 1) the light will be absorbed gradually in the mirror, heating it, and 2) because the universe is unitary, a mode which allows light into the device also allows light out. But you pre-empted this, so lets look at your question.

Silenceisbliss wrote: »

will this increase the temperature inside the sphere with all this mass bouncing around at the speed of light? or will it increase the pressure inside?

Well this depends what is inside the sphere. Assuming there is some matter inside the sphere, you would expect it to come into thermal equilibrium with the em radiation, so that you end up with a black body spectrum. This will almost certainly be in the infra-red, so you will absord all the visible light rather quickly, and be emitting IR instead. If there is no matter then it will come into thermal equilibrium with the mirror walls (effectively being absorbed by them), but you have banned us from considering this option. (It is also relevant to the matter filled case, but would probably not be the dominant effect.) So by banning us from taking absorbtion into account, you have made it impossible to answer your question.

Silenceisbliss wrote: »

if you take said cylinder into a perfectly dark room and smash it, will you see a flash of the light?

Sure, if you managed to break it before the light was absorbed, which will happen really really fast. You can usually expect a couple of percent absorbsion per element in a linear optics setup, even using really good equipment, so say the mirror has at most 95% reflectivity, with the other 5% being absorbed or scattered. After N reflections, we have (0.95)^N of the original photons going unaffected. But the speed of light is really really fast: 3*10^8 m/s. So, if we have a relatively big sphere (say 1m in diameter), in one second it undergoes 3*10^8 reflections, so the fraction of original photons remaining is (0.95)^(3*10^8) which is essentially 0. Even if we take a sphere which could encompass the earth (with a diameter of 15000km, compared to Earths diameter of approximately 12760km) and evacuate all of the gas, in one second it would loose all but 0.95^20 = 0.36 of the light. So, you will never see such an effect.

Silenceisbliss

thanks Fink.

I knew that absorbtion, scatter, and inefficiency would be the cripling elements in this. that's why I wanted them eleminated to a point of where perfect theory is the only componant.

Perfect reflection, no absorbtion, perfect vacume in sphere. these were my criteria.

What you have written basically backs up what I had expected (albeit in more detail and with more superflous vocabulary).

Also, I just noticed that i had written "cylinder" in my last question, my bad.

Thanks for taking the time the time fink.

Professor_Fink

Silenceisbliss wrote: »

thanks Fink.

I knew that absorbtion, scatter, and inefficiency would be the cripling elements in this. that's why I wanted them eleminated to a point of where perfect theory is the only componant.

Perfect reflection, no absorbtion, perfect vacume in sphere. these were my criteria.

No problem.

I couldn't give you an answer fitting exactly within your criteria because they prevent the system from reaching thermal equilibrium, and so there is no well defined temperature for the system. Such states basically break thermodynamics.