Nearsightedness

Or Myopia refers to an eye that can focus only on nearby objects. The far point is not infinity but some shorter distance, so distant objects are not seen clearly. This is caused by an eyeball that is too long or sometimes the curvature of the corn ea is too great. Images of distant objects are focused in front of the retina. A diverging lens causes parallel rays to diverge, allowing the rays to be focused and correcting this defect.
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Farsightedness

Or Hyperopia this is an eye that cannot focus on nearby objects. Although distant objects are usually seen clearly, the near point is somewhat greater then the "normal" 25cm, which makes reading difficult. This is caused by an eyeball that is too s hort or by a cornea that is not sufficiently curved. This is corrected by a converging lens.

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Astigmatism

This is usually caused by an out-of-round cornea or lens, so that point objects are focused as short lines. An astigmatic eye focuses rays in a vertical plane, such as at a shorter distance than it does for rays in a horizontal plane. Astigmatism i s corrected with the use of a compensating cylindrical lens. Lenses for eyes that are nearsighted or farsighted as well as astigmatic are ground with superimposed spherical and cylindrical surfaces, so that the radius of curvature of the correcting lens i s different in different planes.