Flux per unit projected area per unit solid angle,

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Discussion Overview

The discussion revolves around the mathematical expression for "flux per unit projected area per unit solid angle." Participants are exploring the correct formulation and potential typographical errors in a referenced text related to radiometry.

Discussion Character

  • Technical explanation, Debate/contested

Main Points Raised

  • One participant presents the expression L = \frac{\partial \Phi}{\partial \left(cos \Theta \right) \ \partial \Omega} and seeks clarification on its meaning and mathematical validity.
  • Another participant suggests that the expression may be a typo or a non-standard convention, referencing a different formulation found in a table: L = \frac{ \partial^{2} \Phi}{\partial(Acos \Theta) \ \partial \Omega}.
  • A third participant agrees with the second post, asserting that the formulation in the referenced text is likely incorrect and suggests contacting the author for clarification.
  • A fourth participant confirms that they have emailed the author regarding the potential typo.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct formulation, with some believing the original expression is incorrect and others suggesting it may be a convention. The discussion remains unresolved regarding the accuracy of the expressions.

Contextual Notes

There is uncertainty regarding the definitions and conventions used in the referenced material, as well as the implications of the potential typo on the understanding of the mathematical expression.

Somefantastik
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"flux per unit projected area per unit solid angle,"

[tex]L = \frac{\partial \Phi}{\partial \left(cos \Theta \right) \ \partial \Omega}[/tex]

What is this quantity? I mean, I know it's "flux per unit projected area per unit solid angle," how does the math work?

I know it's not

[tex]\frac{\partial \Phi}{\partial (Acos \Theta)} \frac{\partial \Phi}{\partial \Omega}[/tex]
 
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well it's either a typo, or some weird convention where people don't follow the rules. I found a few pages later, a table, where the same quantity was given by

[tex] L = \frac{ \partial^{2} \Phi}{\partial(Acos \Theta) \ \partial \Omega}[/tex]

Which of course, makes a heck of a lot more sense.

It's on page 6 of William Wolfe's intro to Radiometry :-/
 


I think page 6 is a typo- it should be what you have written on post #2. Try emailing William, pointing out the typo- see what he says.
 


Email sent. I can't believe I just did that..
 

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