The first numeral in the couplet refers to the power, or magnification. A pair of binoculars with the numeral 8, for instance, means that whatever you look at through the optic will be magnified eight times the size you would see it with your naked eye.
The second numeral refers to the diameter of the objective lens, which is the end of the binocular facing the animal. The larger that numeral, the greater the diameter of the lensand the more daylight entering the barrel of the optic to illuminate whatever you are looking at.
Putting it all together, then, a pair of 7 x 30 binoculars and a pair marked 7 x 40 will offer the same power of magnification (seven times your naked eye). But the latter pair, with the larger objective lens, will almost certainly give you a clearer, crisper field of vision, especially in low-light situations such as morning and evening, due to the greater light-gathering ability of its lens. No surprise, then, that it will almost surely cost you a bit more.
Over the years I have come to really appreciate the performance of a larger objective lens, since I do so much of my wildlife viewing at dawn and dusk. If I had to choose, for example, between a pair of 8 x 30 binoculars and a pair of 7 x 40, I would take the latter; even with its slightly lower power of magnification, its performance in poor light would still be better than the other pair. To put it another way, having a really powerful magnification factor isn't much of a benefit if the creature you're looking at remains murky and indistinct due to low light.
Before buying a pair of binoculars, make a short list of the situations you will use them in most often. If the top two or three are around my yard, at sporting events, and on short walks in the park close to home, you don't need a pair of binoculars with either high magnification power or an especially large objective lensyou'll be using your binocs in full daylight, over fairly short distances. On the other hand, if your list comes up with such things as for my annual deer hunt, and for watching eagles that nest on the lake by my summer cabin, you will be disappointed with a pair of binoculars that (a) do not perform well in low light and (b) do not magnify well enough to show you whether that deer in the brush at dawn is a buck or a doe, or whether the eagle you're seeing is one of the parents or their young.
Another important factor with binoculars is the overall quality of the glass and other materials that go into it. Quality can be a very big influence on overall performance. In my experience, a high-end pair of 7 x 30 binoculars will always outperform a lesser brand, even if it features higher magnification and light-collecting abilities. Durability is another critical factor. The old adage about getting what you pay for definitely applies to binoculars. There's simply no substitute for high-quality glass and workmanship. But, again, you may not need a high-end pair of binoculars for the activities you pursue most often.
Details mentioned in this article were accurate at the time of publication