Thin-lens optics — UPSC CSE 2004 Physics PYQ

Show that the ratio of the focal lengths of the two lenses in an achromatic doublet is given by \frac{f_1}{f_2} = - \frac{w_1}{w_2} where w_1 and w_2 are the dispersive powers of the lenses of focal lengths f_1 and f_2 respectively.