It's about light transmission, not light gathering. Glass coatings make more difference in light transmission than the size of the lens.
You buy a Zeiss for the glass. A 40mm Zeiss will be brighter than most other scopes out there.
Just goes to show you...a real-life example that size doesn't matter.
TC
That's true, but when we're talking about the objective lens diameter of a riflescope, it's also about exit pupil. When people talk about a big objective being "light gathering," sometimes what they're really talking about is exit pupil.
For example, a 50 mm objective at 9X gives you an exit pupil of just over 5.5 mm -- which is about all the farther the pupil in old eyes will open. So, comparing that to a 40 mm objective at 9X, with an exit pupil of a little less than 4.4 mm, you have a brighter look through the 50 mm lens -- assuming lens coatings and glass quality are equal.
So, one reason for buying a scope with a larger objective lens is to be able to use higher magnification in waning light. Sometimes that's offset by the fact that you need higher rings for objective lens clearance, which might mis-align your eye behind the scope.
Steve