Chapter 35, Problem 49AP

Two lenses made of kinds of glass having different indices of refraction n₁ and n₂ are cemented together to form an optical doublet. Optical doublets are often used to correct chromatic aberrations in optical devices. The first lens of a certain doublet has index of refraction n₁, one flat side, and one concave side with a radius of curvature of magnitude R. The second lens has index of refraction n₂ and two convex sides with radii of curvature also of magnitude R. Show that the doublet can be modeled as a single thin lens with a focal length described by

$\frac{1}{f}=\frac{2n_2-n_1-1}{R}$