Objective size is expressed in millimeters, and is a measurement across the front lens of a scope.
Generally, an optic such as a scope or binocular, will transmit as much light thru it as your eye can accept if the objective lens diameter is 7 times the magnification (power) of the optic.
Going by that formula, a 2.5-10x24 optic would acheive maximum light transmission at the 2.5 end of the magnification range. But only at minimum power.
A 2.5-10 scope with a 40MM objective would acheive maximum light transmission up to about 5-6 power.
Now, on the flip side, the larger objective scopes, like a 50MM objective, have no advantage whatsoever during 95% of your hunting day. Only during those last few minutres of legal shooting time does the larger objective help you.
Frankly, it's been my experience that if you hunt where the regulations allow hunting from dawn to dusk, the huge objectives (50MM +) help very little, if at all- and only at quite high powers.
Illuminated reticles have nothing to do with light gathering. They will help you see the reticle clearly when it's really dark, like for poaching game at 2 AM
Just kidding...an illuminated reticle will help you see the reticle, but it will do nothing to help you find the target in the scope- it actually may hurt a little. The light from the illuminated reticle may fool your eye into thinking there is more light outside than there really is, causing your eye pupil to close down slightly- making everything but the reticle appear darker.