Q.(i) Explain chromatic aberration for spherical lenses. State a method to minimize or eliminate it.

[!TLDR] Chromatic aberration is colour-dependent lens focusing (violet closest); corrected by an achromatic combination -- one converging crown-glass lens with one diverging flint-glass lens -- whose combined focal length matches for the chosen extreme colours. [!ANSWER] (i) Chromatic aberration = different foci per colour (dispersion in refraction); minimized/eliminated with an achromatic doublet. …

1. CHROMATIC ABERRATION: because a lens material's refractive index (and hence, via the lens maker's equation, its focal length) differs by colour, a lens forms a slightly DIFFERENT focus for each colour of a polychromatic beam like white light -- a convex lens behaves like two thin prisms joined base-to-base, so violet (deviated most by the higher-index-for-violet material) focuses CLOSEST to the lens, and red focuses FARTHEST, with intermediate colours' foci spread out between them. This produces a circle of least confusion rather than one sharp point image, exactly analogous to spherical aberration but caused by colour dependence rather than aperture. It is minimized/eliminated using an ACHROMATIC combination of two lenses (see part ii).
2. ACHROMATISM is the correction of chromatic aberration for a chosen pair of extreme colours (typically violet and red), achieved by combining two lenses of different materials so their combination's resultant focal length is identical for both chosen colours. For two thin lenses of dispersive powers omega1, omega2 held in CONTACT, requiring f_V = f_R for the combination and applying the lens maker's equation to each lens for each colour leads, after algebra, to the ACHROMATISM CONDITION K1/K2 = -[omega1(n2Y-1)] / [omega2(n1Y-1)], where K = 1/R1 - 1/R2 for each individual lens. Since dispersive power omega is always POSITIVE, this condition forces K1 and K2 to have OPPOSITE signs, i.e. one lens must be CONVERGING (convex) and the other DIVERGING (concave) -- chromatic aberration cannot be corrected using two lenses of the same sign. For the overall achromatic combination to remain net CONVERGING, the higher-di …

Explain chromatic aberration's cause (colour-dependent refractive index via the two-prisms-base-to-base model), then derive the achromatism condition for two lenses in contact by equating f_V=f_R via the lens maker's equation for each colour, …

Stating that achromatism requires two lenses of the SAME sign (both convex, say), rather than correctly deriving that the positive-dispersive-po …