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Homework Help: Radiative transfer equation: Intensity from a disk.

  1. Nov 18, 2009 #1
    Hello to everyone who reads, and thank you very much.

    1. Problem:
    The actual problem is this: A thin disk with thickness 2H and radius R (H<<R), has an absorption co. "alpha" and emision co. j.
    Calculate the intensity I("miu", "tau"), where "miu" = cos("theta"), and "theta" is the angle from the disk normal, and "tau" is the optical depth in the vertical direction ("tau" = "alpha" * 2H).

    2. Relevant equations
    1. Radiative transfer equation: dI/ds = -"alpha"*I + j (ds = length element along a ray)
    2. d("tau") = "alpha" * ds
    3. "miu" = cos("theta")

    3. The attempt at a solution
    My biggest problem is that my understanding of the meaning of intensity is very weak.
    I am thinking in the direction of looking at a specific ray coming from a certain "hight" z, compared to the bottom of the disk, coming in angle "theta", and solving the equation above for it, and then summing the effect of all rays, or something.
    I could do this and more, but there are some really fundemental things I do not understand and would really appreciate answers:

    The transfer equation, as I understand, is describing intensity behaviour for a specific ray, right? But how do I sum up the effects of several rays?
    Is it meaningful to ask "what is the intensity at the point P"? What happens if 2 rays with intensity I arrive to a point P? What is the intensity in P then?
    We have studied intensity is constant along a ray. How come then, the intensity in any point in space isn't infinite, giving intensity comes from everywhere and remains constant?
    I realize these questions might be rather silly and much more basic than the question but I really cannot solve them.
    Once I understand these, I might know how to handle the question. I just don't understand if I'm suppose to sum up all the effects of rays going out of the disk in direction "theta" from the normal.

    Thank you very very much, I'd really appreciate help here, I'm lost (and I've been reading the book over and over but I just cannot grasp it).

  2. jcsd
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