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If we ignore lasers you can't focus light to make it any brighter than where it started. And because as something gets hotter it starts to radiate it is impossible to focus light onto a point and make that point hotter than the light source.
Because lasers work differently the rules are different.
Can you explain the reason? I don't know how to prove it.
I don't think it is possible to focus all the light from the source down any smaller than it's own size, but my optics isn't good enough to proove this I am afraid.
Quote from: lightarrow on 13/02/2008 13:04:14Can you explain the reason? I don't know how to prove it.I am not sure I can prove it off the top of my head without resorting to thermodynamics, If you could could focus the heat radiation from a large flat thing to a point, and make this point very hot, you could then run a heat engine from this point back to the large cool flat thing - essentially a perpetual motion machine.I think optically it is to do with how small you can make an image of an object compared to how much light you are collecting... I am had waving now but isn't on extreme of focusing an ovoid with your source at one focus and another object at the other?[diagram=316_0]Now all the light emitted from the source will hit the second object, but the image will be the same size as the source and because it will start emitting too, when it gets to the same temperature as the source it will be loosing exactly the same amount of heat as it is gaining.I don't think it is possible to focus all the light from the source down any smaller than it's own size, but my optics isn't good enough to proove this I am afraid.
Ok, thank you Dave, you were quite convincing
Thermodynamics has got to be the answer. You can't get owt for nowt, as they say. But I haven't got it straight yet.In an ellipsoid mirror, objects at the two foci must reach equilibrium (i.e. each one losing the same energy that it was gaining), if no energy is lost on reflection in the walls of the mirror.But, if they have different areas, then the smaller object would have to be at a higher temperature than the larger one, for this to happen. A small bright white object and a large red hot object - sounds like nonsense.
A bit of a paradox, in fact.Lightarrow, please resolve this for me (or any other plucky young person).On second thoughts, I think it might be ok; both objects would be radiating and absorbing the same amount of energy but the big object might have more internal energy - because of its thermal capacity.
If you draw a sphere around your 'pointlike object' then the illumination of one sphere (watts per square cm) will only depend on the surface area of the sphere. N'est pas?
it's not the same since the sphere surface emits also in the direction perpendicular to the sphere's radius, and those light beams don't all focus on the other foci.
Quoteit's not the same since the sphere surface emits also in the direction perpendicular to the sphere's radius, and those light beams don't all focus on the other foci.But, for a big enough ellipsoid and small enough spheres, what you say is less and less relevant; each point on the surface is an omnidirectional (hemispherical) radiator but the effective sum in any one direction will be the same as from a central point; I think it is the equivalent to the gravitational potential of a spherical shell compared with a central point mass. My Watts per square cm flux idea still holds, I think.I don't think that has resolved the paradox yet.