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Math Help - Connection between two Solid Agnles!!!

  1. #1
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    Connection between two Solid Agnles!!!

    Hi all,

    I have a question regarding the connection between two solid angles. Let assume a solid angle Q and another solid angle F on the surface of two spheres. One sphere has a unit radius and the other sphere has some other radius bigger than one. Therefore the solid angle subtended by a surface area on the sphere of larger radius should be smaller than the solid angle subtended by the surface area on the sphere with radius=1. I assume that the surface area is common to both spheres. What is the connection between the two solid angles?

    In other words how can I express the solid angle of Q (bigger radius) in terms of the solid angle of F(unit radius)?

    I would appreciate your help

    Best Regards

    Alex
    Last edited by tecne; March 3rd 2008 at 02:03 PM.
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  2. #2
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    Quote Originally Posted by tecne View Post
    I have a question regarding the connection between two solid angles. Let assume a solid angle Q and another solid angle F on the surface of two spheres. One sphere has a unit radius and the other sphere has some other radius bigger than one. Therefore the solid angle subtended by a surface area on the sphere of larger radius should be smaller than the solid angle subtended by the surface area on the sphere with radius=1. I assume that the surface area is common to both spheres. What is the connection between the two solid angles?

    In other words how can I express the solid angle of Q (bigger radius) in terms of the solid angle of F(unit radius)?
    The solid angle by definition is the surface area divided by the square of the radius. So if the two surface areas are the same then the solid angle of Q will be the solid angle of F divided by the square of the larger radius.
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