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Calculating steradians (solid angle)

  1. Sep 17, 2014 #1

    jmc

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    1. The problem statement, all variables and given/known data
    For a sphere of radius r, find the solid angle Ω in steradians defined by spherical angles
    of: a.) 0°≤θ≤ 20°, 0°≤ø≤360°;


    2. Relevant equations
    dA = r2 sin dθ dø (m2)
    dΩ = dA / r2 = sin dθ dø (sr)

    3. The attempt at a solution
    I think I understand what a steradian (sr) is, on a sphere, and I need to find what ratio of a 4∏ is formed by the above limits, but I can't make the connection on how to form that ratio. ?
     
  2. jcsd
  3. Sep 17, 2014 #2

    SteamKing

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    First, draw a sketch of the region. I assume you are familiar with spherical coordinates?
     
  4. Sep 17, 2014 #3

    jmc

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    I have tried to sketch it. What I see is.the top portion of the sphere, sliced where 20 deg from the X-axis meets the edge of the sphere.
    But how to convert that to a steridian, I still don't see.

    Thank you
     
  5. Sep 18, 2014 #4

    SteamKing

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    You have to go back to the definition of what the steradian represents:

    http://en.wikipedia.org/wiki/Steradian

    In other words, you got some calculatin' to do. You know the region for which the steradian is desired, now you have to calculate the values of the quantities in the formula for the steradian.
     
  6. Sep 18, 2014 #5

    nrqed

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    You do not need to take any ratio. You simply have to integrate ## d \Omega ## over the section you are considering.
     
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