ay45c3-page13

ay45c3-page13 - In either case our nal result is P = 1u 3...

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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 speci c 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 speci c intensity is constant, but the solid angle subtended by the given object decreases in such a way that the inverse square law is recovered.  37  ...
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