Your eye is basically a light focusing system. Rays of light enter your eyes, and the combination of your cornea and your lens focus the rays onto a structure called the retina, which is located at the back of the eye. If your eye focuses light exactly on the retina, you have good vision and see things sharply. People who are farsighted or nearsighted have eyes with properties that lead to light not being focused exactly on the retina. In nearsighted people, the light focuses on a point in front of the retina, whereas in farsighted people, light focuses at a point behind the retina. In both cases, because light is not perfectly focused on the retina, objects appear blurry (‘out of focus’).
In an eye exam, the eye doctor is basically determining what kind of extra lens (glasses or contacts) is needed so that the combination of the extra lens + your actual eye will lead to light being focused exactly onto the retina, thus restoring sharp vision. The + and – of a prescription are related to whether you’re nearsighted or farsighted and basically mean whether the lens will move the point at which light rays focus forward or backward. If your natural eye causes light to focus behind the retina, you need a lens that will move the focal point forward onto the retina. If your natural eye causes light to focus in front of the retina, you need a lens that will move the focal point backward onto the retina.
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