Steradian: -- F.Sc. (Class 11) Physics Important Student Learning Output (SLO) based Notes

Q. Define Steradian.

Answer:

Steradian is a three-dimensional solid angle and is defined as " the angle subtended at the center of the sphere, by which the surface area of the sphere is equal to the square of the radius of that sphere", as shown in the figure below and it is equal to the ratio between the subtended spherical area to the square of the radius. It is denoted by 'sr'.

Angle θ = `\frac {(Spherical area)}{r^2}`(sr) 

But the spherical area = 4πr²

θ = `\frac {4πr^2}{r^2}` (sr)

θ = 4π (sr)  ------------ (1)

θ = 4ｘ 3.1416 (sr)

θ = 12.5664 (sr) -------------(2)

Equations (1) and (2) show that there are 4π, or approximately 12.5664, steradians in a complete sphere.

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