Amount Of Light VS Lens Size ?

[wedgy]

Is there a formula to compare how much more light I would gain from a larger objective, given all else is equal ? For example a 5x power scope with a 42mm objective(5542 sqmm) compared to a 50mm(7854 sqmm) is ~40% more area and a
56mm(9852 sqmm) is ~78% more area.
Any idea how much more visible light one would gain ? I'm pretty sure it's not a simple surface area calculation, if I even got those right. My knowledge in this area is limited but I'm pretty sure somebody here is a rocket scientist in optics. This forum is full of them !

And with binoculars how would a set of 10x50mm compare to an 8x50mm or a 7x 50mm, again same brand, lens, etc. only difference being the lens size ?

Please enlighten me.

 

[ericbc7]

As I understand it (from chuck Hawks) doubling the objective size quadruples the light transmitted; I.e. A 50 mm obj transmits 55%. More light than a 40 mm obj. Some trade offs are larger objectives = higher paralex potential, shallower depth of field and obligatory higher mounts - smaller objective = lower resolution.

The quality of the glass makes more difference I think. The question is what benefit can the human eye discern vs practical advantage of smaller optics?

 

[gunsandgunsmithing]

Research "exit pupil".