This is wrong OP. Larger diameter = MORE light at a given power.2. More diameter, less light at given power.
For the ranges you're talking about a fixed power scope would also be a workable option, something like 4X. No zoom will give you a better performing optic for the money. Just like a prime camera lens will ALWAYS be better performing than any zoom lens. Zoom lenses are always a compromise in some area. (I usually always buy 3-9 or 4-10/12 for the flexibility offered, but your intended use is different than mine.)
50mm is pretty big and you'll have to ensure you get the proper height scope rings. I have 50's and they are larger and heavier than the 40mm equivalents. But they're also a bit brighter in low light conditions, because of the larger diameter lens out front.
Eye relief is a separate measurement that isn't necessarily related to either the objective or the magnification of the scope.
JMR "may" be correct about the 50 vs. 40mm at the higher magnifications, however that depends on the design of the optics and I think the better scopes are brighter at higher levels of magnification with larger objectives. But I don't design scope optics so I'm not willing to argue he is wrong on that point.
I own both the Leupold VX3's and Nikon Monarch's and find they are brighter and clearer than their lower priced brothers and hence, worth the extra money.
Edited to add: Here is a pretty useful link with well presented and simple information that may help you. http://www.myoan.net/tipstricks/riflescopeterm.html
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