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)

$6 : 5$

Answer 2

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,
$\omega_{2}=\frac{14^{\circ}-10^{\circ}}{12}=\frac{1}{3}$
$\frac{\omega_{1}}{\omega_{2}}=\frac{2}{5} \times \frac{3}{1}=\frac{6}{5}$