Two prisms A and B are in contact with each other have angular dispersion of $2^o$ and $4^o$ respectively The dispersive power of 'A' is 0.002. If the combination produces dispersion without deviation that dispersive power of 'B'

The correct option is D $0.004$

Angular dispersion of prism A = $2^{\circ }$

Angular dispersion of prism B = $4^{\circ }$

Dispersive power of A = $\frac{{\left({\delta }_V-{\delta }_R\right)}_A}{{\delta }_A}$

$\Rightarrow 0.002=\frac{2^{\circ }}{{\delta }_A}$

$\Rightarrow {\delta }_A=\frac{2^{\circ }}{0.002}$

As there is no deviation, ${\delta }_A={\delta }_B$

Dispersive power of B $=\frac{{\left({\delta }_V-{\delta }_R\right)}_B}{{\delta }_B}=\frac{4^{\circ }}{2}\times 0.0002={0.004}^{\circ }$

The dispersive power of B is 0.004.