# JEE Main & Advanced Physics Ray Optics Dispersion Through a Prism

Dispersion Through a Prism

Category : JEE Main & Advanced

The splitting of white light into it's constituent colours is called dispersion of light.

(1) Angular dispersion $(\theta )$: Angular separation between extreme colours i.e. $\theta ={{\delta }_{V}}-{{\delta }_{R}}=\mathbf{(}{{\mu }_{V}}-{{\mu }_{R}}\mathbf{)}A$. It depends upon $\mu$ and A.

(2) Dispersive power $(\omega )$:

$\omega =\frac{\theta }{{{\delta }_{y}}}=\frac{{{\mu }_{V}}-{{\mu }_{R}}}{{{\mu }_{y}}-1}\text{ where }\left\{ {{\mu }_{y}}=\frac{{{\mu }_{V}}+{{\mu }_{R}}}{2} \right\}$

$\Rightarrow$It depends only upon the material of the prism i.e. m and it doesn't depends upon angle of prism A

(3) Combination of prisms : Two prisms (made of crown and flint material) are combined to get either dispersion only or deviation only.

(i) Dispersion without deviation (chromatic combination)

$\frac{A'}{A}=-\frac{({{\mu }_{y}}-1)}{(\mu {{'}_{y}}-1)}$

${{\theta }_{\text{net}}}=\theta \,\left( 1-\frac{\omega '}{\omega } \right)=(\omega \delta -\omega '\delta ')$

(ii) Deviation without dispersion (Achromatic combination)

$\frac{A'}{A}=-\frac{({{\mu }_{V}}-{{\mu }_{R}})}{(\mu \,{{'}_{V}}-\mu \,{{'}_{R}})}$

${{\delta }_{\text{net}}}=\delta \,\left( 1-\frac{\omega }{\omega '} \right)$

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