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Answer to Question #6094 in Optics for Mohammed Samir

Question #6094
what is the relation between focal length and refractive index of a lens?
Expert's answer
The focal length of a lens is determined by its refractive index n and the radii of curvature R1 and R2 of its surfaces. The power of a thin lens in air is given by the Lensmaker's formula:
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" 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