Wish we had an edit feature, but here is a cool experiement that you can try. if you can get a hold of some broken point and shoot cameras. (I usually get them from the fleamarket (great way to get electronics that you can salvage parts from.
take a small point and shoot camera lens and get a larger point and shoot lens, then using some paper under them point the lens at the sun. both will give a similarly sized spot, but the larger lens will start a fire while the small one will just get very hot. (also why they tell you to never point your camera at the sun.)
A larger lens physically captures more light and focuses it on a smaller area, the end result is better low light performance from a larger lens. Light is largely physical and is limited. The hard way of getting a better exposure is making a more sensitive sensor which can take what little light there is and provide a higher gain without adding too much extra noise.
A lower tech but more expensive way to do it is to use more glass. have a larger lens gather more light and focus it on the sensor
Here are some images:
Small lens roughly half the size of the larger one:
[ur]http
/i.imgur.com/rnN7npz.jpg[/url]
Now here is the larger lens:
http://i.imgur.com/YEEfbFu.jpg
(in this image you see 2 rings, that is caused by the flash light, the lens on the flash light causes 2 rings and the the center ring of light at such a close range to the lens is not enough to fill it so judge the size by the outer ring
both cameras which used the 2 different lenses, had an 8mm sensor the difference is 1 camera had a zoom function and the other did not
The end result is the larger lens focuses more light on the same amount of space.