Thursday 22 November 2018

Conservation of etendue

Here's why you can't focus thermal light sources like the sun to a point which would get hotter than the emitting surface of the light source (omnidirectional thermal emitter). This would also violate the laws of thermodynamics. Here's what happens if you try...
...no arrangement of lenses, mirrors or any passive elements allows focusing beyond the surface temperature of the source.
Lenses and parabolic mirrors rather than purely focusing, make an image which has a minimum size that is proportional to the distance of the thermal source and the intensity lost to distance balances the sheets so that focusing alone can't result in hotter spot than the surface of the emitter.

So no matter how large a magnifying glass, even the size of earth, your spot won't get hotter than the surface of the sun. It's just equalization of temperature between two objects assisted by the magnifying glass in a way similar to bringing the objects closer to each other.
However, pure unidirectional emitters like lasers don't exactly have to obey this kind of limit. High temperature corresponds to high entropy and high disorder, whereas in terms of entropy, laser light is highly ordered, but unlike cold systems which are void of energy, laser is a kind of saturated form of energy from which energy can always flow away to increase the entropy of a typical thermodynamic system. Classical thermodynamic systems can't have this sort of state as their entropy can always increase. Only certain well isolated systems can be temporarily driven to this kind of saturated state by external source of energy.

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