Lens is generally used either to converge or to diverge the rays of light. Generally lenses are made from materials having refractive indices greater than unit. In air, convex lens converges whereas concave lens diverges the light rays. When the refractive index of lens is greater than the surrounding medium convex and concave lenses behave as stated above. In general refractive index of lens refractive index of medium surrounding the lens . But, in case refractive index of lens is either equal or less than the refractive index of surrounding medium , convex and concave lenses behave differently than mentioned above. Table-1 below summarizes the behavior of lenses under different conditions.
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Behaviour of lens under varying circumstances
1. Lens in different refractive index : http://www.askmattrab.com/notes/193-lens-in-surrounding-of-different-refractive-medium
2. Cutting of lens : http://www.askmattrab.com/notes/194-cutting-the-lens-in-different-shapes
3. Combination of lens : http://www.askmattrab.com/notes/195-combination-of-lens
4. Silvering of lens : http://www.askmattrab.com/notes/196-silvering-of-lens