10×40 means that everything looks 10 times bigger then without the binoculars and have a 50mm lens to collect light. You may also see a field of view label measured in how wide the image is at 1000m or a certain number of degrees. If you buy another 10×40 with a wider field of view the image will look the same but the dark ring limiting your vision will be wider so you can easier scan the landscape without having to move the binoculars. But you can also get a pair of 7×40 binoculars which will have improved field of view over your existing ones but not because the dark ring is larger but because you can see more things through it. This is like zooming out on a camera.
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