Created By : Naaz Fatima

Reviewed By : Rajashekhar Valipishetty

Last Updated : May 10, 2023


Make use of the Deviation and Dispersion Formulas listed over here to understand the concepts thoroughly in a quick manner. Get acquainted with the Deviation and Dispersion Formulae and apply them while solving your problems to get instant solutions. You can get instant help regarding various concepts using the Physics Formulas Collection of ours. In this Formula Sheet of Deviation and Dispersion, you can get Formulas related to Dispersion, Cauchy's Formula, Dispersion without deviation, etc.

Important Deviation and Dispersion Formulae

A → Angle of prism
δ → Angle of deviation
╬┤ = i + e – A
A = r1 + r2
Deviation & Dispersion formulas img 1

1. Condition of no emergence

┬╡ > \(\frac{1}{\sin A / 2}\) > cosec(A/2)
Condition of Grazing Emergence (means = e = 90┬░)
r2 = ╬╕c
i = sin-1 [\(\sqrt{\mu^{2}-1}\) sin A – cos A]
Condition of max. deviation
Deviation will be max. when imax = 90┬░
╬┤max = 90┬░ + sin-1 [┬╡ sin (A – ╬╕c)] – A
Condition for min. deviation
it occur when i = e, r1 = r2 = r & A = r/2
╬┤min = (2i – A)

2. Prism formula

┬╡ = \(\frac{\sin \left(\frac{\delta_{\min }+A}{2}\right)}{\sin A / 2}=\frac{\sin \left(\frac{\delta_{\min }+A}{2}\right)}{\sin A / 2}\)
For thin prism
deviation ╬┤ = A(┬╡ – 1)

3. Dispersion

Splitting of a beam of white light into its constituent colours.

4. CauchyΓÇÖs formula

┬╡ = A + \(\frac{C}{\lambda^{4}}+\frac{C}{\lambda^{4}}\)
A, B & C are constants.

5. Angular dispersion

╬╕ = ╬┤v – ╬┤r = (┬╡v – ┬╡r) A

6. Dispersive power

\(\frac{\theta}{\delta_{y}}=\omega=\frac{\mu_{\mathrm{v}}-\mu_{\mathrm{r}}}{\mu_{\mathrm{y}}-1}=\frac{\Delta \mu}{\mu-1}\)

7. Conbination of prisms

Deviation & Dispersion formulas img 2
net deviation
╬┤ = ╬┤1 – ╬┤2
╬┤ = (┬╡1 – 1) A1 – (┬╡2 – 1) A2
net angular dispersion
╬┤v – ╬┤r = (┬╡1v – ┬╡1r) A1 – (┬╡2v – ┬╡2r) A2
= (┬╡1y – 1)╧ë1A1 – (┬╡2y – 1)╧ë2A2

8. Dispersion without deviation

╬┤y = o, (┬╡1y – 1) A1 = (┬╡2y – 1)A2
╬┤v – ╬┤r = ╬┤1 (╧ë1 – ╧ë2) = ╬┤2 (╧ë1 – ╧ë2)

9. Average deviation without dispersion

╬┤v – ╬┤r = 0
(┬╡1y – 1) ╧ë1A1 = (┬╡2y – 1) ╧ë2A2
╬┤ = ╬┤1\(\left(1-\frac{\omega_{1}}{\omega_{2}}\right)\)
╬┤1 = (┬╡1y – 1) A1

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