Thermal Equilibrium of Lens and Disk in Solar Projection

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Homework Help Overview

The discussion revolves around the thermal equilibrium of a disk when exposed to solar radiation through a lens. The problem involves concepts from optics and thermodynamics, specifically focusing on how the lens affects the temperature of the disk by altering the solar flux received.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • The original poster seeks guidance on how to begin the problem, indicating uncertainty about the initial steps. Some participants inquire about the scenario without the lens, suggesting a comparison of approaches. Others mention having calculated the temperature based on flux comparisons, raising questions about the role of the lens in modifying solar flux.

Discussion Status

The discussion is active, with participants exploring different aspects of the problem. Some have provided calculations related to the disk's temperature, while others are questioning the implications of using a lens. There is no explicit consensus, but productive inquiries are being made regarding the effects of the lens on solar flux.

Contextual Notes

Participants are navigating the assumptions related to the setup, including the distances involved and the properties of the lens. There is a focus on understanding how these factors influence the thermal behavior of the disk.

nicu15
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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
 
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How would you do the problem if there was no lens?
 
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 said:
How would you do the problem if there was no lens?
nicu15 said:
I've already done that part.
... good.

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

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