Suppose I were in a perfect mirrored glass sphere (with the mirror on the inside surface). Suppose I had a light.
Would the mirror prevent photons from escaping the sphere? Would the light get brighter and brighter? What would happen when I turned the light out?
Cheers
G.
If you’re in the sphere, your body will be absorbing some of the light. So the light would get brighter until the rate of absorption by your body equals the rate your flashlight emits light.
Some past threads on the subject:
https://boards.straightdope.com/sdmb/showthread.php?t=820727
Per Spider Robinson, if you ask a bunch of people this question, they will confidently begin to answer, and then fall silent and after a short bit, change the subject.
I have a confident answer which will not cause that result: The light will dim very, very quickly because of, essentially, quantum phenomena, specifically the fact there are no perfect mirrors, only objects which lose some visible light to heat at every reflection.
End result: The visible light dims very quickly, essentially instantly from a human perspective, and you end up with a somewhat warmer hollow sphere which is pitch black inside.
You can argue that I’m ignoring the conditions. Well, yes, because the conditions are nonphysical. This is a thought experiment, and thought experiments which go tits-up are often a way to gain insight into what a new theory has to do. Einstein famously used the thought experiment of riding a beam of light to come up with Special Relativity.
Here’s a good article on how mirrors work in Scientific American, and, yes, there’s always loss.
Now that the main question has been answered, let’s look at how close you can get in real life.
Laser: In an ideal laser you have a perfect mirror on one end, and a 99.9…% mirror on the other. In steady state you have a lot of identical photons bouncing around inside, and a much smaller stream forming the output laser beam. The “Q factor” is a measure of the mirror quality (at least partially). For the really badass lasers, they generate so many & such high energy photons that you don’t need a mirror; in fact a mirror would probably absorb enough photons to melt.
Integrating sphere: Non-mirrored, white sphere with tiny openings for input and output. You use them as part of measuring the power in a light source. Until I read the wiki, I didn’t know there is a reflecting version (Coblentz sphere) - that’s probably the closest you’ll get.
Blackbody source: In this one the ideal sphere is black, completely absorbing (I wonder if anyone’s used the new graphene stuff in one yet). You heat it up, and the light coming out is the thermal spectrum of whatever the temperature is.
Optical fiber: For the most part, light doesn’t go through the fibre like water down a pipe. The light is actually coming in at a shallow angle, so it bounces back and forth like a rubber ball down a pipe. It uses “total internal reflection” to be a very very good mirror. Not sure how many bounces it gets, but enough that you can easily send a signal 20ish km and still receive it. Back of envelope, on the order of 10000000000 reflections
Actually, the question Robinson asked was “If you are at the center of a perfect mirrored sphere, what would you see?”, not exactly the OP’s question.
the mirrored surface would absolutely prevent light from escaping, provided it was a good and complete coating. That’s what mirrors do. The surface would reflect most of the light, but inevitably some would be absorbed and some scattered. So the light wouldn’t get “brighter and brighter” , except on a really short time scale. The light level would pretty rapidly reach a steady state with the flashlight providing light and the walls (and your body) absorbing the rest. When you turn the light off, it goes dark so rapidly you wouldn’t notice any sort of lag.
As a rule of thumb, the number of reflections you get is about R/(1 - R), where R is your reflectivity. If your mirror reflects 0.999 (that’s 99.9%) of the light, you’ll get 1000 bounces before it’s gone – and that’s ignoring the light YOU absorb. If you work out how long that will take, given whatever size sphere you’re using, you’ll find it’s just this side of zero time.
as for Robinson’s question – what’s at the center of the sphere? Your head or the center of your body? If the former, you’ll have an image of your head placed right at your head – so it’ll be severely out of focus, because you have to be a little distance away from something to see it. If your middle’s at the center of the sphere you’ll see an out-of-focus image of your feet.