That ratio has more to due with exit pupil size (ie the amount of light that can get to your eye) than with eye strain. Most healthy humans pupils can't dialate past 7mm and this decreases as we age. If the bino's exit pupil is larger than your pupil that extra "light gathering" is wasted.The rule of thumb I always heard is the objective lense divided by the power should be 5 or higher. That means 8x40 and 10x50. This is to reduce eye strain. That being said, I am sure higher quality glass with a smaller objective will accomplish this also. I'm in your price range and prefer my leupold cascades in 8x40. I have used them in many situations and always find them to be adequate.