Average Pressure Radiation on Perfectly Absorbing Surface

[rugerts]

Homework Statement

A light source radiates a sinusoidal electromagnetic wave uniformly in all directions. This wave exerts an average pressure p on a perfectly reflecting surface a distance R away from it. What average pressure (in terms of p) would this wave exert on a perfectly absorbing surface that was twice as far from the source?

Homework Equations

pressure radiation of perfect absorber = (Intensity)/(speed of light)

pressure radiation of perfect reflector = (2 * Intensity)/(speed of light)

Intensity = (Power)/(Area)

Surface Area of Sphere = 4*pi*R^2

The Attempt at a Solution

Since you probably can't see that, here's an imgur link: https://imgur.com/a/uxltWGV

When I try to do the math, I get that it's a factor of 1/8. But, if I try to reason through it, it seems like 1/4 is a reasonable answer since I'm just doubling a square factor.

Thanks for your time.

 

[haruspex]

since I'm just doubling a square factor.

You are doubling the distance factor, which is squared, but you are also getting afactor of 1/2 from the absorption. Where's the puzzle?

 

[rugerts]

You are doubling the distance factor, which is squared, but you are also getting afactor of 1/2 from the absorption. Where's the puzzle?

The puzzle is that I get an answer of 1/8 and an answer I found online is 1/4.

 

[haruspex]

The puzzle is that I get an answer of 1/8 and an answer I found online is 1/4.

Please post the link.

 

[rugerts]

Please post the link.

http://www.slader.com/textbook/9780321696861-sears-and-zemanskys-university-physics-with-modern-physics-13th-edition/1074/discussion-questions/12/

 

[rugerts]

Please post the link.

?

 

[haruspex]

http://www.slader.com/textbook/9780321696861-sears-and-zemanskys-university-physics-with-modern-physics-13th-edition/1074/discussion-questions/12/

The question discussed at that link considers two perfectly reflecting surfaces. The question in post #1 of this thread compares a reflecting surface with an absorbing one.