^Chromatic aberration

(a) Various colors in white light get dispersed at various points on the principal axis resulting in a large no. of blurred images.

(b) Longitudinal chromatic abb. = f_R – f_V =df = – ωf

(c) For a combination of two lenses separated by a distance x to produce achromatism.

If lenses are in contact, then x = 0 & condition of achromatism becomes.

This is possible only if one is convex & other is concave. Also this implies ω ∝ f. In order to produce a convergent achromatic beam from a combination of a convex & concave lens in contact the lens having more focal length must have more dispersive power (more refractive index).