Determine Radiation pressure given the fraction of total absorption

[MrMoose]

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

 

[voko]

So how do you go from Pra and Prr to total pressure?

 

[MrMoose]

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