Physics - Geometrical Optics Question with Solution | TestHub

The dispersive power of a prism is given by $\omega =\frac{{\delta }_b-{\delta }_r}{{\delta }_y}$

The mean deviation ${\delta }_y$ is the average of the deviations of the blue and red rays: ${\delta }_y=\frac{{\delta }_b+{\delta }_r}{2}$

For prism A:
${\delta }_b=12^{\circ }$, ${\delta }_r=10^{\circ }$
${\delta }_{yA}=\frac{12^{\circ }+10^{\circ }}{2}=11^{\circ }$
${\omega }_A=\frac{12^{\circ }-10^{\circ }}{11^{\circ }}=\frac{2}{11}$

For prism B:
${\delta }_b=10^{\circ }$, ${\delta }_r=8^{\circ }$
${\delta }_{yB}=\frac{10^{\circ }+8^{\circ }}{2}=9^{\circ }$
${\omega }_B=\frac{10^{\circ }-8^{\circ }}{9^{\circ }}=\frac{2}{9}$

The ratio of their dispersive powers is:
$\frac{{\omega }_A}{{\omega }_B}=\frac{\frac{2}{11}}{\frac{2}{9}}=\frac{9}{11}$

Answer: $9:11$