Question

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

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

Answer 1

The correct option is C $6:5$

For prism 1,
$\delta =\frac{{\delta }_B+{\delta }_R}{2}=\frac{12+8}{2}=10$
$[given,{\delta }_R=8,{\delta }_B=12]$
$\therefore {\omega }_1=\frac{{\delta }_B-{\delta }_R}{\delta }=\frac{12-8}{10}=\frac{4}{10}=\frac{2}{5}$
For prism 2,
$\delta =\frac{{\delta }_B+{\delta }_R}{2}=\frac{14+10}{2}=12$
$[given,{\delta }_B=14,{\delta }_R=10]$
$\therefore {\omega }_2=\frac{{\delta }_B-{\delta }_R}{\delta }=\frac{14-10}{12}=\frac{1}{3}$
So, $\frac{{\omega }_1}{{\omega }_2}=\frac{2/5}{1/3}=\frac{6}{5}$