What is a convex lens?
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A lens (from the Latin for "lentil seed," which has the characteristic thick in the middle and thin at the edges shape) is any piece of glass or other transparent material with at least one curved surface. A convex lens is a class of lens that causes light passing through it to converge, as opposed to the class of concave lenses, which cause light passing through them to diverge. Where the light converges after passing through a convex lens is termed the focus; the distance between the focus and the center of the lens itself is called the focal length. The shorter the focal length on a convex lens, the more drastically the light is bent to meet at the focus, and the more powerful the lens.
Understanding Physics, I. Asimov, pg 31, Barnes & Noble, 1966.
The lens with a curved shape is named a convex lens; in fact, a convex lens has a bulky center and thin edges. A convex lens inverts the image and it's used to bring a small image closer. That's why convex lenses are often used as magnifying glasses--because of their property to make things look bigger.
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