Stargazing Solid angle acceptance of a muon telescope

AI Thread Summary
The discussion centers on calculating the solid angle acceptance of a muon telescope consisting of two aligned square detector panels. One method proposed involves using the solid angle of a pyramid formed by the detectors, while another suggests a formula of (x squared)/(L squared). The consensus leans towards the latter approach, especially when the distance between detectors (L) is significantly greater than their size (x). It is noted that while the corners of the detectors perceive slightly different solid angles, this variation is typically negligible in practical applications. The conversation emphasizes deriving the solid angle from first principles and the implications of small angle approximations.
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I am trying to work out the solid angle acceptance of a muon telescope. The telescope is comprised of two aligned square detector panels (of size x squared metres) set at a distance apart of L metres. The way I was initially working it out (by using the solid angle of a pyramid of base x squared and height 0.5L, containing [as I thought] all the possible muon tracks through the telescope) is completely different to that which my friend insists is the right way (a solid angle defined by [(x squared)/(L squared)]).

Any help on how to find the solid angle from first principles and a resultant equation?
 
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Remember it's all possible tracks through the distant square to a single point on the near detector.
Assuming the detectors are much further apart than their size then x^2/L^2 sounds right.
 
And how would you derive that?
 
From the definition of solid angle. And by assuming that sin(a) = a for small angles.
 
Ok, so you have all possible tracks going through the first detector to a single point on the second detector (effectively a pyramid) but what about the tracks that hit the second detector outside of the point?
 
For any given point on the 2nd detector there is the same area of initial of detector 1 at the same distance and so the same solid angle.
The corners of the detectors do see slightly different solid angles and so the corner-corner angle is larger - this is normally ignored if L is much greater than the size of the detector.
In optical detectors it would correspond to the maximum angle vs the unvignetted angle.
 
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