KCET · Physics · Ray Optics
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 \(5: 6\)
- B \(9: 11\)
- C \(6: 5\)
- D \(11: 9\)
Answer & Solution
Correct Answer
(C) \(6: 5\)
Step-by-step Solution
Detailed explanation
Dispersive power, \(\omega=\frac{\delta_{B}-\delta_{R}}{\delta}\)
For 1st prism,
\[
\begin{aligned}
\omega_{1} &=\frac{\delta_{B}-\delta_{R}}{\delta} \\
&=\frac{12^{\circ}-8^{\circ}}{10^{\circ}}=\frac{2}{5}
\end{aligned}
\]
where \(\delta=\frac{\delta_{B}+\delta_{R}}{2}\)
Similarly, for 2 nd prism,
\[
\begin{aligned}
\omega_{2} &=\frac{14^{\circ}-10^{\circ}}{12}=\frac{1}{3} \\
\therefore \quad \frac{\omega_{1}}{\omega_{2}} &=\frac{2}{5} \times \frac{3}{1}=\frac{6}{5}
\end{aligned}
\]
For 1st prism,
\[
\begin{aligned}
\omega_{1} &=\frac{\delta_{B}-\delta_{R}}{\delta} \\
&=\frac{12^{\circ}-8^{\circ}}{10^{\circ}}=\frac{2}{5}
\end{aligned}
\]
where \(\delta=\frac{\delta_{B}+\delta_{R}}{2}\)
Similarly, for 2 nd prism,
\[
\begin{aligned}
\omega_{2} &=\frac{14^{\circ}-10^{\circ}}{12}=\frac{1}{3} \\
\therefore \quad \frac{\omega_{1}}{\omega_{2}} &=\frac{2}{5} \times \frac{3}{1}=\frac{6}{5}
\end{aligned}
\]
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