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The solid angle is defined by a region by the rays of a sphere, and is measured as
Where,
A_{n} is projection of incident surface normal to line of propagation.
Solid angle is represented by α.
The plane angle is defined by a region by the rays of a circle, and is measured as\
Where,
L is arc of length and r is radius of circle.
It is the ratio of arc of length on the circle to the radius of the circle.
When the incident surface is a sphere, the projection of surface normal to the line of propagation is the silhouette disk of the sphere which is a circle of the diameter of
It must be a circle of diameter of a sphere.
If I _{n }denotes the normal intensity and I _{α} represents the intensity at angle α, then
The intensity of radiation in a direction from the normal is proportional to cosine of the angle.
The intensity of normal radiation I _{n} is how much times the emissive power?
I _{n }= σ T^{ 4}/ π and E = σ T^{ 4}.
A small surface emits diffusively, and measurements indicate that the total intensity associated with emission in the normal direction I _{n }= 6500 W/square m sr. The emitted radiation is intercepted by three surfaces. Mark calculations for intensity associated with emission
For a diffusion emitter, the intensity of the emitted radiation is independent of direction.
Consider a deepspace probe constructed as 1 m diameter polished aluminum sphere. Estimate the equilibrium temperature that the probe reaches if the solar energy received is 300 W/m^{2}. For solar radiation, absorptivity of aluminum is 0.3 and the average emissivity appropriate for aluminum at low temperature is 0.04
Q _{in }= α q A _{P} = 70.7 W. Q _{out }= E σ _{b }A T ^{4}.
The total emissive power of the emitter with area d A and temperature T is given by
E = I _{n }π d A.
A black body of 0.2 m^{2} area has an effective temperature of 800 K. Calculate the intensity of normal radiations
I_{n }= α T ^{4}/π = 7396.28 W/m^{2} sr.
The energy radiated out decreases with increases in α and becomes zero at an angle of
I _{α }= I _{n} cos α. So at 90 degree it becomes zero.
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