Although lens can be cut in random ways and hence its properties will change accordingly, but, here properties of lens have been summarized when it is cut symmetrically along optical axis and along the principal axis. The two symmetrical cut have been shown in Fig.-1.
(i) A symmetric lens is cut along optical axis in two equal parts. Intensity of image formed by each part will be same as that of complete lens. Brightness of image formed by cut lens will be same as complete lens.
(ii) A symmetric lens is cut along principle axis in two equal parts. Intensity of image formed by each part will be less compared as that of complete lens. (Aperture of each part is 1⁄√2 times that of complete lens). In this case brightness of image formed will be halved than that of complete lens.
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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