Consider a thin symmetrical biconcave lens made of glass of refractive index 1.5, each surface having radius of curvature 30cm.
(i) Starting from the relation for refraction at a spherical surface, derive an expression for the focal length of a thin biconcave lens in terms of the refractive index of the material and the radii of curvature of its two surfaces. State clearly the sign convention adopted.
(ii) Using the expression obtained in part (i), calculate the focal length of the given lens and state whether it is positive or negative.
(iii) An object is placed 15cm in front of this lens. Compute the position, nature and magnification of the image formed.