Question

A prism of a certain angle deviates the red and blue rays by $8^{\circ }$ and $12^{\circ }$ respectively. Another prism of the same angle deviates the red and blue rays by $10^{\circ }$ and $14^{\circ }$ respectively. The prisms are small angled and made of different materials. The dispersive powers of the materials of the prisms are in the ratio

• A. $11:9$
• B. $6:5$
• C. $9:11$
• D. $5:6$

Answer 1

Answer: (B)

Dispersive power, $\omega =\frac{{\delta }_B-{\delta }_R}{\delta }$
For 1st prism,
${\omega }_1=\frac{{\delta }_B-{\delta }_R}{\delta }$
$=\frac{12^{\circ }-8^{\circ }}{10^{\circ }}=\frac{2}{5}$
where $\delta =\frac{{\delta }_B+{\delta }_R}{2}$
Similarly, for 2 nd prism,
${\omega }_2=\frac{14^{\circ }-10^{\circ }}{12}=\frac{1}{3}$
$\frac{{\omega }_1}{{\omega }_2}=\frac{2}{5}\times \frac{3}{1}=\frac{6}{5}$