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Unformatted text preview: focal
plane eyepiece
D δθ δθ d p eyeball angle δϕ l L D is the aperture; L is the focal length of the objective lens; d is the exit pupil; l is the eyepiece focal
length The basic idea is that the objective makes an image at the focal plane,
and the eyepiece is simply a \magnifying glass" for looking at that image.
From the gure you can derive M = magnication = ' = L :
l
Notice that it is useless to have d bigger than p (the pupil size of the human
eye, no greater than about 9 mm when dark adapted) because the extra rays
simply do not enter the eye! Tracing the rays back, the maximum useful size
of D is
D = Md Mp :
Bigger than this does not make a brighter image (Liouville's theorem, again).
Smaller than this does make a dimmer image. How can this be true without
violating Liouville? Answer: for ray bundles of diameter smaller than p, the
eye is no longer a good approximation to a \surface brightness meter"  it
is articially \stopped down." (In bright light, of course, the eye naturally
stops down on its own, when the pupil contracts.)
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 Fall '09
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