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Irradiance of sun in an image?

  1. Mar 18, 2014 #1
    1. The problem statement, all variables and given/known data

    What will be the irradiance (power per unit area) in the image, if the Sun's irradiance at the sea level is I = 500W/m^2

    Lens is 200mm f
    Sun is 150x10^9 m away
    Diameter of sun is 1.4x10^9 m


    2. Relevant equations



    3. The attempt at a solution

    I know that at the lens the irradiance will be the same i.e. 500W/m^2 but at the image the irradiance will be magnified. I'm not sure how to get there though.
    I know an image of the sun will be .2m from the lens and the diameter of the image will be .00187m because M=di/do = .2m/150x10^9 = 1.333X10^-12 and 1.333x10^-12 multiplied by the diameter of the sun is .000187m.
     
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  3. Mar 18, 2014 #2

    haruspex

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    What's the total power falling on the lens? What's the total power in the image?
     
  4. Mar 19, 2014 #3
    I'm not sure how to find the diameter of the lens which is what I need to find the total power falling on the lens
     
  5. Mar 19, 2014 #4
    I think that the radius of the lens is equal to 2f which would make the radius .4m. Therefore, the area of the lens is .50265m^2. Multiply this by 500 and this tells you the power on the lens which is 251.327W. The area of the image is 1.099X10^-7m^2 which is from ((.000187m)^2(pi)). Therefore, 251.327W also falls on this same area and dividing 251.327W by the area of the image (1.099X10^-7m^2) will give you the power per m^2 which is 2.29X10^9 W/m^2

    Is this correct?
     
  6. Mar 19, 2014 #5

    haruspex

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    Good point. Then I don't see how you can answer the question. carnivalcougar gives a way to find an upper bound, since the focal length sets a limit on the diameter of the lens. But it will depend on the refractive index.
     
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