Angular Chromatic Dispersion

The refractive index of  the material of a prism is given by



where A is the angle of the prism and θ is the angle of minimum deviation.



If dθ is the difference in the angle of deviation between two spectral lines of wavelengths λ and λ + dλ, then dθ/dλ is called the angular dispersion between the wavelengths λ and λ + dλ.

Differentiating equation (i) with respect to on the left hand side and θ the right hand side.



Dividing by dλ





d/dλ is called chromatic dispersion of the material of the prism. The angular dispersion of the material of a prism depends on the angle of the prism and refractive index of the material of the prism. Using a spectrometer and the given prism, a graph is drawn between and λ ( along the Y-axis and λ along the X-axis). The tangent to the curve at any point measures the chromatic dispersion d/dλ for that particular wavelength. Substituting this value of d/dλ in equation (iv), dθ/dλ can be calculated.

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