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Solid angle

  1. Sep 21, 2009 #1
    why solid angle is A/r^2 ....why is this r^2....has it any similarity with s=rtheta??plz help me
     
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  3. Sep 21, 2009 #2

    Meir Achuz

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    They are similar.
    Angle is defined as theta=s/R, where s is an arc length and R the radius of a circle.
    Solid angle is defined as Omega=A/R^2, where A is an area on a sphere and R is the radius of the sphere.
    In each case, the angle and solid angle are dimensionless, but given the names radian and steradian for convenience.
    If the surface is not on a sphere, then differential vectors must be used in the definition of solid angle.
     
  4. Sep 21, 2009 #3
    why u r using r^2..it is just to make the whole thing dimestionless or any other physics in it..??
     
  5. Sep 21, 2009 #4

    clem

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    It does make solid angle dimensionless, but there are other reasons too.
    Why divide s by R for radians? Because the arc length is proportional to R.
    Dividing the arc length by R makes the angle measure in radians independent of the size of the circle. The same reasoning gives R^2 for steradians, because the area isl proportional to R^2. This is all simple mathematics, independent of any physics.
     
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