I've narrowed my choice for a new scope to the Zeiss conquest. Either 4.5-14x50 or 3-12x56. I'm very new really getting in-depth on optics. And just want some options. All the scopes I currently have are x50 and when I look though x40's I see a big difference. Thanks!
Actually, the benefit depends on the magnification and your age. For example, a 50 year old person has a maximum eye pupil size of about 6 mm in low light (i.e., for dark adapted eyes). As long as the exit pupil of the scope is larger than your eye pupil, the image will be as bright as viewing with the naked eye.
The exit pupil size is equal to the objective size divided by the magnification. For a 50 mm objective the exit pupil is 6 mm (i.e., the same size as the eye pupil) at a magnification of 8.3X. For a 56 mm objective the magnification is 9.3X at a 6 mm exit pupil size. At a magnification below about 8x both scopes have the same brightness for a 50 year old person. But at the same exit pupil size of 6 mm, the larger scope provides a12% higher magnification.
At higher magnifications, the ratio of exit pupil area to eye pupil area determines the brightness. For example, at a magnification of 12X, the smaller scope is (4.16/6)^2=48% as bright as the naked eye, and the larger scope is (4.67/6)^2=60% as bright as the naked eye. So, at 12X the larger scope is 25% brighter (as LouBoyd said).
If you do a lot of hunting in low light the larger objective can be worth the extra cost and weight.
I prefer the smaller lens every time big objectives require extra high rings/modified cheek pieces etc to get a good fit also if shooting from any position other than prone. good luck shouldering said modified rifle. It depends on the use of the rifle. if shooting off a bench at paper/steel then the sun is most likely out so you wont need added light transmission if you are specifically shooting long range at low light from fixed position then yes bigger would be better. All my current scopes are under 50mm when it gets darker i turn the scope down 40mm/6x is 6.6 exit pupil shots I have taken at this time of day always seem to be under 200 yards anyway. All that said I am looking for a high magnification scope of quality and most seem to come with 50mm or bigger objectives.....
No idea what math formula you are following?? But its sure not "area=pi r squared"???
It's true that is the formula for finding the area of a circle, but when comparing the areas of 2 different circles the constants and common factors in the expression will cancel. So you can use diameter, radius, or 57.35 times the radius of each circle and you will arrive at the same ratio when finished...which in this case is a ratio of 1.2544:1. So there is 25.44% more area on a 56mm lens when compared to a 50mm.
It's really a trade off though. Bigger, heavier, and usually more expensive is the price you pay for having a brighter image at dusk and dawn.