A glass prism deviates the red and violet rays through $9^{\circ}$ and $11^{\circ}$ respectively. A second…
A glass prism deviates the red and violet rays through $9^{\circ}$ and $11^{\circ}$ respectively. A second prism of equal angle deviates them through $11^{\circ}$ and $13^{\circ}$ respectively. The ratio of dispersive power of second prism to first prism is
$5: 6$
$6: 5$
$9: 13$
$13: 9$
Solution
$\therefore \quad$ Dispersive Power of Prism:
$\begin{aligned}
& \omega=\frac{\delta_v-\delta_r}{\delta_y} \\
& \delta_y=\frac{\delta_v+\delta_r}{2}=\frac{11+9}{2}
\end{aligned}$
$\therefore \quad$ For first Prism,
$\begin{aligned}
\omega_1 & =\frac{2(11-9)}{11+9} \\
& =\frac{1}{5}
\end{aligned}$
For Second Prism:
$\begin{aligned}
\omega_2 & =\frac{2(13-11)}{13+11} \\
& =\frac{1}{6}
\end{aligned}$
Ratio:
$\frac{\omega_2}{\omega_1}=\frac{\frac{1}{6}}{\frac{1}{5}}=\frac{5}{6}$
$\therefore \quad$ The ratio is $5: 6$.