Q.What is dispersive power? Find the necessary conditions for obtaining deviation without dispersion by two thin prisms.

Let’s start with something you’ve seen: a glass prism splitting white light into a rainbow. That band of colours — violet, indigo, blue, green, yellow, orange, red — is called a spectrum. The prism does this because different colours travel at slightly different speeds inside the glass, so they bend by different amounts when entering and leaving the prism. Red bends the least, violet the most.

Now ask yourself: if you had two different prism materials — say, crown glass and flint glass — which one would spread the colours wider? That’s the question dispersive power answers. It’s a number that tells you how strongly a material separates colours, relative to the average bending it produces.

The precise definition

For a prism, the deviation (bending) of a ray depends on the refractive index $n$ of the material. Since $n$ is different for each colour, we get different deviations. Let:

• $n_v$ = refractive index for violet light (extreme end of the visible spectrum)
• $n_r$ = refractive index for red light (the other extreme)
• $n$ = refractive index for some mean colour — usually yellow (the sodium D-line), which lies roughly in the middle of the visible spectrum.

The angular dispersion produced by the prism is the difference in deviation between violet and red rays. For a thin prism (small apex angle $A$), deviation $\delta = (n-1)A$, so:

But a material that bends light more overall (higher $n$) will also tend to spread colours more. To compare materials fairly, we divide the angular dispersion by the mean deviation $\delta = (n-1)A$:

This ratio $\omega$ is the dispersive power. It is a dimensionless number, independent of the prism’s shape or size — it depends only on the material.

What the formula tells you

• The numerator $n_v - n_r$ is the absolute spread of refractive indices across the visible spectrum. A larger difference means more colour separation.
• The denominator $n-1$ is the mean deviation factor — how much the prism bends the central colour. Dividing by it normalises the spread, so you’re measuring the material’s relative ability to disperse, not just its absolute bending.

So a material with high dispersive power (like flint glass, $\omega \approx 0.03$) spreads colours widely even if its mean deviation is modest. A material with low dispersive power (like crown glass, $\omega \approx 0.015$) gives a narrower spectrum for the same mean deviation.

A common exam nuance …