What is the solid angle subtended by the hemisphere at centre? 4π steradian 2π steradian π steradian 3π steradian
Question
What is the solid angle subtended by the hemisphere at centre?
- 4π steradian
- 2π steradian
- π steradian
- 3π steradian
Solution
The solid angle subtended by a hemisphere at its center is 2π steradians.
Here's the step by step explanation:
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A solid angle measures the amount of the field of view from some particular point that a given object covers. It is measured in steradians.
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For a full sphere, the solid angle at the center is 4π steradians. This is because a sphere has 360 degrees of freedom, and when this is converted into radians (since 1 radian = 180/π degrees), we get 4π steradians.
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However, a hemisphere is just half of a sphere. Therefore, the solid angle it subtends at its center is half of that of a full sphere.
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Hence, the solid angle subtended by a hemisphere at its center is 2π steradians.
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