In your first example, 10 refers to the magnification being 10 times the actual size of the viewed object. The 40 is the diameter of the large lens at the front.
10 X 50 is usually the largest common size. It’s just about at the limit of what can be held steadily by hand. Anything bigger would almost certainly need a tripod or hide-clamp to be usable.
You might want to consider a small telescope.
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