ay45c3-page5 - Example Compare photons close to and far...

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Unformatted text preview: Example: Compare photons close to and far from an extended source like a star: star photons here are crowded in physical space (high density) but spread out in solid angle (direction) photons here are diffuse in physical space (low density) but highly collimated in angle (high density). So, dilution of photon density is always accompanied by increased collimation in a precise quantitative relationship! 3.1.3 Brightness Let's compute the total energy dE in a small volume of phase space dE = EdN = E N d3 x d3p 1 E 2 dE d = c3 = E 3N =c2 d2 dt dE d E N (cd2  dt)      Id2 dt dE d : Here we have de ned I = N E 3=c2 : We see that I is the energy in photons per (normally incident) area per time per solid angle per photon energy interval dE. I is called the \speci c intensity" or \brightness" of a radiation eld at a particular point, in a particular direction, at a particular energy. 29 ...
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