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Re: (meteorobs) 1X "binoculars" ? idea/question

Dustin,

Your idea for a 1x "telescope" that just amplifies your LM, is not 
theoretically possible, regardless of the size of the objective you 
plan to use. Here is why. Magnification (M) is the ratio of your 
objective focal length (F) over your eyepiece focal length (f). so, 
M=F/f.
From geometrical optics, you can see that the exit pupil (p) (which 
is the area at the output end of your eyepiece, in which all the 
objective's light is concentrated) is related to the eyepiece focal 
length (f) just as the objective diameter (D) is related to the 
objective focal length (F). So, p/f=D/F. Rearranging the equality, we 
get D/p=F/f. But F/f is just M, so we get D/p=M.
So, basically, the magnification also equals the ratio of your 
objective diameter to your exit pupil. For 1x magnification,  the 
objective diameter must equal the exit pupil (D/p=1). Now, since 
your eye has a typical maximum dark-adapted pupil diameter of 
7mm, it means that the scope exit pupil should not exceed 7mm. 
Any wider exit pupil from the scope "wastes light", because your 
eye is unable to accept a wider input. So, that means your 
objective diameter cannot exceed 7mm, either, for 1x 
magnification, if you dont want to waste any light. For example, if 
you use a 10" (254mm) objective (LM~14.2), at 1x, the exit pupil 
would also be a whopping 10". Your 7mm eye pupil would only 
intercept 7mm^2/254mm^2 = .00076 = .076% of the light from the 
objective.  You are losing (100%-.076%)  99.924% of the 10" 
objective light, which is equivalent to about 7.7 magnitudes, so the 
LM~14.2 drops back to normal naked eye LM~6.5.

So, in summary, you cannot gather more light than the maximum 
size of your eye pupil allows in, using any passive optical system 
with 1x magnification.
If you want to see fainter LM, get an image intensifier, etc.

Thats the story,
Mike.

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