Q.Refractive index of a flint glass varies from 1.60 to 1.66 for visible range. Radii of curvature of a thin convex lens are 10 cm and 15 cm. Calculate the chromatic aberration between extreme colours.

Because refractive index (and hence a lens's focal length, via the lens maker's equation) varies with colour, a lens forms a slightly DIFFERENT focus for each colour of a polychromatic beam -- CHROMATIC ABERRATION. A convex lens behaves like two thin prisms joined base-to-base, so violet (deviated most) focuses closest to the lens, red (deviated least) farthest, with a resulting circle of least confusion rather than one sharp point.

Chromatic aberration cannot be eliminated for all colours at once, but it CAN be corrected for a chosen extreme pair (typically violet and red) using an ACHROMATIC combination of two lenses -- either held in contact or suitably separated. Requiring the combination's resultant focal length to be identical for both chosen colours, and applying the lens maker's equation to each colour, yields an ACHROMATISM CONDITION relating the two lenses' curvature factors $K=\frac1{R_1}-\frac1{R_2}$ to their dispersive powers $\omega$. Since $\omega$ is always positive, this condition forces one lens to be CONVERGING …