Unformatted text preview: In either case, our nal result is P = 1u :
3
The pressure of isotropic radiation is exactly 1/3 its energy density. 3.3.5 Example: Sphere of uniform brightness [From Rybicki and
Lightman]
Let us calculate the ux at an arbitrary distance from a sphere of uniform
brightness I = B (that is, all rays leaving the sphere have the same brightness). Such a sphere is clearly an isotropic source. At P , the specic intensity
is B if the ray intersects the sphere and zero otherwise.
I=B θ
R P θc
r Then, Z F = I cos d = B 2 Z 0 d c Z 0 sin cos d ; where c = sin 1 R=r is the angle at which a ray from P is tangent to the
sphere. It follows that F = B (1 cos2 c) = B sin2 c
or 2
F = B R :
r
Thus the specic intensity is constant, but the solid angle subtended by the
given object decreases in such a way that the inverse square law is recovered.
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 Fall '09
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