Two prism $\text{A}$ and $\text{B}$ in contact with each other. The dispersive power of $\text{A}$ and $\text{B}$ is $0.04$ and $0.03$ respectively. The angular dispersion produced by $\text{A}$ is $8^{\circ }.$ The angular dispersion produced by the combination, if the combination does not produce a net deviation is-

The correct option is D $2^{\circ }$
Given,

${\omega }_A=0.04;{\omega }_B=0.03;{\theta }_A=8^{\circ }$

For dispersion without deviation,

$\frac{{\theta }_A}{{\omega }_A}+\frac{{\theta }_B}{{\omega }_B}=0.......\left(1\right)$

Where, ${\theta }_A,{\theta }_B$ and ${\omega }_A,{\omega }_B$ are angular dispersion and dispersive power of $\text{A}$ and $\text{B}$ respectively.

From (1) we get,

$\frac{8}{0.04}=\frac{{\theta }_B}{0.03}$

${\theta }_B=2\times 3=6^{\circ }$

The net angular dispersion is,

$\theta ={\theta }_A\sim {\theta }_B=8^{\circ }-6^{\circ }=2^{\circ }$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(D\right)$ is the correct answer.