Subject: Can a Lens focus light to the temperature of the sun?

In my mind, since we are talking about energy per unit square, as long as we 
increased the tightness of the focus, temperature would tend toward infinity.  
It is just a matter of adding enough energy into the system.  Why am I right or 
wrong?  Question: You're at your son's camp and he and his friends have been 
playing with magnifying glasses. (You know... burning stuff.) You start fooling 
around with the magnifying glasses yourself. You notice that when you focus the 
sun's energy on your hand with the bigger lens  which you can see has a shorter 
focal length  it burns more quickly than when using the smaller lens. You 
mention to another "camp Dad" that if you had a big enough lens with a tight 
enough focus, you could create a hot spot on a target which would be hotter 
than the surface of the sun. He bets you can't. Who's right?  Answer: You can't 
do it. This is a radiative heat transfer problem, where energy flows from one 
body to another, from a higher temperature to a lower, following the equation q 
= c(Tsun^4 - Tsurf^4) where c is a constant and q is the heat flow rate. Heat 
flows from the hotter surface to the (relatively) cooler surface according to a 
fourth power law. Since the driving energy source is the sun itself, the best 
you could ever hope to do would be for the focused spot's temperature to 
asymptotically reach Tsun, at which point there would be no net heat flux.

Re: Can a Lens focus light to the temperature of the sun?