An achromatic doublet is a lens designed to minimize chromatic aberrations. It typically consists of a lowdiSpersion glass lens and a highdispersion glass lens fused together. In this problem we would like to design an achromatic doublet that focuses collimated blue (A = 400 nm) and red (A = 700 nm) light to the same point on the Optical axis, as shown in the gure below. You may assume that refracting surfaces are thin, that prOpagation between them is negligible, and the refractive index everywhere outside the lens is no = 1. y (a) Using ray transfer matrices (ABCD matrices), nd the system matrix M E R2X2 that describes the system including the doublet lens followed by prOp agation by distance d. Simplify as much as possible. (b) Use the matrix to derive a condition for collimated light focusing at a dis tance d. (c) Given that n1(400 nrn) = 1.4, n1(700 11m) = 1.2, n2(400 nm) = 2.2, n2(700 nm) = 1.4 and d = 500 mm, solve for the radii of curvature, R1 and R2