Thermal Equilibrium of Lens and Disk in Solar Projection

[nicu15]

Lens & Disk

The image of the sun is projected on the disk using a lens of radius r<<d and focal length f<<d (d is the distance between the sun and the disk.. The magnification of the lens is M`f/d, so that the image completely fills the disk R`=MR. When the disk reaches thermal equilibrium, what is its temperature?

I don't really know where to start, so a hint would help a lot.

Thanks

 

[Simon Bridge]

How would you do the problem if there was no lens?

 

[nicu15]

I've already done that part.

Computed the flux in and compared it with the flux out of the disk. got a temperature of $T_{disk}=T\sqrt{\frac{R}{d}}$ where d is the distance from the sun to the disk and R is the radius of the sun.

 

[Simon Bridge]

How would you do the problem if there was no lens?

I've already done that part.

... good.

So what does the lens do in terms of the solar flux that gets to the disk?