other people in the above have been given correct explanation. This is my take:
The starting point is that human eyes can only have 7mm pupil, so anything more than 7mm is a waste. you are just carrying glass unnecessarily. there are some 4x50 scopes out there, for example.
Things get a little interesting then you have a variable power scope. with a given sized objective glass, obviously when you wind the power down you get more light to your eye. But again the most your eye can get 7mm, so if you have a 4-12x42, you will fine the scope get brighter as you move down power, but it should get no brighter past 6x power.
This does not mean, however, 6x power is the best. Arguably while you get more light you get less magnification, so you may well find, despite of it being brighter, it is harder for you to see your target, and you may well find 12x power gives you a better view, dimmer but clearer.
The math simply means that you get no gain by going below 6x power.
In real life people have different pupil sizes and as they age they lose the pupil size at different rate. Some people maintain 6.x mm even into their 60s, while others do not. So to have a practical value of this particular knowledge you really need to go out in twilight and play with your variable scope to find out what power works for you. If you are over mid-30s, your pupil may well have lost its best flexibility, you may well find yoruself seeing no brightness difference between 6x to 7.5x on a 42mm lens.
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