Wednesday, February 17, 2010

Solid angle

Solid angle ( Ω )는 어떤 물체가 어떤 점에서 마주 보고 있는 3차원 공간의 2차원 각도이다. 이것은 그 점에서 관찰하고 있는 관찰자에게 그 물체가 얼마나 크게 보이는지 측정하는 것이다. 가까운 작은 물체는 먼 곳의 더 큰 물체와 동일한 solid angle을 가지고 있을 수 있다. 물체의 solid angle은 물체에 의하여 제한되는 단위 구의 일부분의 영역과 동일하다. Solid angle은 단위 구의 segment 영역과 동일하며, 이것은 단위원의 호의 길이에 planar angle이 동일한 것과 같다.

Solid angle의 단위는 SI에 따르면 steradian(sr)이라고 불리운다. 수학과 물리학의 관점에서 보면, solid angle은 dimension과 단위가 없으며, 따라서 "sr"은 과학적인 관점에서 생략되어야 한다. 어떤점에서 안쪽으로 측정된 solid angle은 4π sr이고, solid angle은 cube의 가운데에서 한 면을 마주보고 있는 solid angle은 1/6이거나 2π/3 sr 이다. Solid angle은 square degree (1 sr = (180/π)2 square degree) 구의 부분으로 설명될 수 있으며 1 sr = 1/4π이다.

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