Suppose the light source is a black body with average temperature 2000K, and I want to use it to heat another black body to 2500K, via passive devices only. Here passive device means lens, mirror, medium... anything that doesn't actively do work.
I understand I can't focus the light beam unlimitedly small under geometrical optics' framework, my question is actually regarding thermodynamics. The second law of thermodynamics said that this is not possible, I cannot create temperature higher than the light source itself, otherwise this is a second-kind perpetual motion machine. The best I can do is a temperature equal to 2000K.
Now here is my question: can I use an absorbing medium, cut down low frequency and keep the high frequency part of the spectrum only, to make the spectrum that just shapes like 2500K? (but less total energy, of course) Can I use this "fake" 2500K spectrum heat the blak body to higher than 2000K? If the answear is yes, does this violates the second law of thermodynamics?