JEE Main & Advanced Physics Ray Optics Dispersion Through a Prism

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)

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

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