Question

Derive the relation between the focal length of a convex lens in terms of the radii of curvature of the two surfaces and refractive index of its material. Write the sign conventions and two assumptions used in the derivation of this relation.

Answer 1

For thin lens approximation there is the following formula for the focal length:
1/f = (n-1) [1/R₁ - 1/R₂],
where f is the focal length, n is the refractive index, R₁,R₂ - radii of the curvature of refracting surfaces. The derivation of this formula you can find in any book in Optics.