Dispersion By A Prism

Dispersive power measures how strongly a material spreads colours relative to its average bending, defined as $\omega =\frac{n_v-n_r}{n_y-1}$, where $n_v$, $n_r$ and $n_y$ are the violet, red and mean (yellow) refractive indices. Crucially the prism angle cancels for a thin prism, so $\omega$ depends only on the material. The spread of indices is $n_v-n_r=1.532-1.514=0.018$, and the mean deviation factor is $n_y-1=1.523-1=0.523$. Therefore $\omega =\frac{0.018}{0.523}\approx 0.034$. The deeper significance is that dispersive power separates the two distinct roles a prism plays: $(n_y-1)A$ governs the average bending of the beam, while $(n_v-n_r)A$ governs the spreading of colours; their ratio strips away the geometry and leaves a pure material property. This is exactly why an achromatic combination pairs a crown-glass prism with a flint-glass prism of differing dispersive powers so their colour spreads cancel while a net deviation survives. The value 0.018 is wrong because it is only the numerator $n_v-n_r$ and omits division by the mean term. The value 0.090 is wrong as it represents the angular dispersion $(n_v-n_r)A$ for a 5° prism, not a dimensionless power. The value 0.052 is wrong because it mistakenly divides by $n_v-1$ inconsistently. This is the NCERT definition underlying achromatic prism combinations. A consistency check confirms dispersive power is a small dimensionless number around a few percent for ordinary crown glass, matching 0.034.