Q.Explain and define dispersive power of a transparent material. Obtain its expressions in terms of angles of deviation and refractive indices.

[!TLDR] Dispersive power omega = (angular dispersion)/(mean deviation) = (n_V - n_R)/(n_Y - 1), a dimensionless property of the prism material alone (independent of A). [!ANSWER] omega = (delta_V - delta_R)/delta_Y = (n_V - n_R)/(n_Y - 1); dimensionless, depends only on the material's refractive indices, not on prism dimensions.

Dispersive power is defined as the ABILITY of a transparent material to disperse (angularly separate) its constituent colours -- formally, for any two chosen colours, it is the RATIO of the angular dispersion between them to the MEAN deviation for those same two colours. Taking violet and red as the extreme colours, and yellow as the conventional mean colour, the mean deviation is delta_Y = A(n_Y - 1) (from the thin-prism formula), and the angular dispersion is delta_VR = A(n_V - n_R) (derived above). Dividing these: omega_VR = delta_VR/delta_Y = [A(n_V-n_R)] / [A(n_Y-1)] = (n_V - n_R)/(n_Y - 1) -- the prism angle A cancels out entirely, showing that omega is a property of the MATERIAL alone, not of any particular prism's physical dimensions. Being a ratio of two like angular quantities (or, equivalently, of two dimensionless refractive-index differences), omega is itself dimensionless and unitless. Ordinary crown glass has omega around 0.03; dense flint glass has a considerably higher omega, around 0.10 -- which is exactly why flint glass is chosen whenever strong, clearly visible dispersion (e.g. in a spectrometer prism) is specifically wanted, and why achromatic lens combinations deliberately pair a low-omega crown-glass element with a high-omega flint-glass element. [!ANSWER] omega = delta_VR/delta_Y = (n_V-n_R)/(n_Y-1); dimensionless, a pure material property (prism angle cancels out).

Define dispersive power as angular dispersion divided by mean deviation, substitute the thin-prism formulas for each, show the prism angle A cancels leaving only refractive indices, and note the resulting expression is dimensionless.

Leaving the prism angle A in the final expression for omega, missing that it cancels out algebraically, which is exactly what makes dispersive power a material property rather than a prism-specific one.