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This is a follow up question to an earlier one asked. I understand now that natural sunlight cannot be focused to heat a target up to the temperatures needed to ignite the target to fuse. But, that leads to the next part. Incoherent radiation has a focal limit. From my understanding of it, because the surface of the Sun has a temperature of 5800 K, the light cannot be focused to an intensity more than that temperature unless the light is coherent.

Am I understanding this correctly? That the only way to concentrate the sunlight to a intensity where the temperature is higher than 5800 K is to somehow make the radiation coherent? (I.E. a laser or electron current of some type)? Also, how does one calculate the maximum intensity that incoherent radiation can be concentrated to?

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The temperature only applies to a thermal black-body source. If you get the light from a hot object you can't focus it to heat an object to a higher temperature because then the light from the now hotter object would flow back to the source.

Coherent radiation doesn't have a temperature in the same way so the law doesn't apply. The maximum temperature of an object heated with lasers is generally limited by it staying together. We can heat objects to fusion temperatures (100,000,000 K) with lasers today.

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