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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 nrism to first prism is
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Verified Answer
The correct answer is:
$5: 6$
$\therefore \quad$ 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 $5: 6$.
$$
\begin{aligned}
& \omega=\frac{\delta_v-\delta_r}{\delta_y} \\
& \delta_y=\frac{\delta_v+\delta_r}{2}=\frac{11+9}{2}
\end{aligned}
$$
$\therefore \quad$ 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 $5: 6$.
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