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Homework Help: Optics question

  1. Jan 6, 2006 #1
    Hi guys

    I'm flicking thorugh some past papers for an upcoming exam and came across this seemingly easy problem.

    "The average intensity of solar radiation at the Earth is 1.4kW/m^2. Assuming the earth is a perfect absorber, calculate the force exerted by the radiation on the surface of the Earth. The mean radius of the earth is 6400 km"

    Now I know that the radiation pressure on a perfect absorber is equal to the energy density, which is equal to the intensity divided by the speed of light.

    [tex] P = U = \frac{I}{c} [/tex]

    Given that P=F/A I get that the force should be.

    [tex] F = \frac {IA}{c} = \frac {I 4\pi R^2}{c} [/tex]

    Although it could be [tex] \frac {I 2\pi R^2}{c} [/tex]

    As the sunlight only directly hits approximately half of the Earth's surface. But either way, when I plug in the numbers I don't get the answer my Lecturer gave of 600 MN.

    I must be missing something, but I can't see it. If any of you guys can I'd appreciate it.:biggrin:
     
  2. jcsd
  3. Jan 6, 2006 #2

    Doc Al

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    Staff: Mentor

    Since the sunlight is essentially parallel, the area of interest is that of a circle (not a hemisphere or sphere).
     
  4. Jan 6, 2006 #3
    That makes sense, since I had noticed I was out by a factor of 4, I just couldn't come up with the physical meaning.

    Thanks Doc Al
     
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