Determine Radiation pressure given the fraction of total absorption

AI Thread Summary
The discussion focuses on calculating radiation pressure on an object that absorbs a fraction of incident radiation and reflects the rest. The radiation pressure due to total absorption is given by Pra = (frac)*I/c, while the pressure from total reflection is Prr = 2*(1 - frac)*I/c. To find the total radiation pressure, the two pressures are combined, resulting in the equation Pra + Prr = (2 - frac)*I/c. The confusion arises from understanding how to derive the total pressure from the individual components. Ultimately, the correct total radiation pressure formula is confirmed as Pra + Prr = (2 - frac)*I/c.
MrMoose
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Homework Statement



Radiation of intensity I is normally incident on an object that absorbs a fraction frac of it and reflects the rest back along the original path. What is the radiation pressure on the object?

Homework Equations



Radiation pressure Pr (force/unit area)

Pra = I/c (total absorption)

Prr = 2I/c (total reflection back along path)

The Attempt at a Solution



The object absorbs a fraction frac of the intensity, which I translate mathematically as:

Pra = (frac)*I / c

This would mean that the total intensity reflected is:

Prr = 2*(1 - frac)*I/c

Unfortunately the answer is: Pra = (2 - frac)*I / c

I don't know how they came to this conclusion. Thanks in advance, MrMoose
 
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So how do you go from Pra and Prr to total pressure?
 
Holy smokes. Thanks.

Pra + Prr = (frac)*I/c + 2*(1-frac)*I/c = I*frac/c + 2*I/c - 2*frac*I/c

= (2 - frac)*I / c
 

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