The dispersive power of a grating is defined the ratio of the difference in angle of diffraction of any two neighbouring spectral lines to the diffraction in the wavelength between the two spectral lines. It is expressed as dθ/dλ

We know (a+b) sinθ = nλ

Differentiate with respect to λ

[(a+b)cosθ] dθ/dλ=n

dθ/dλ= n / [(a+b)cosθ] dispersive power of grating

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1.Higher is the order, greater is the dispersive power
2.Smaller is the grating element, more widely spread is the spectrum.
3.If the value of θ is large, cosθ will be small and therefore dispersive power will be more.
We know λ(Red) > λ(Violet)
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Therefore angle of diffraction for Red light is greater than Violet in a given order spectrum, therefore the dispersion in the red region is greater than that in violet region.