MHT CET · Physics · Ray Optics
A glass prism ' \(A\) ' deviates the red and blue rays through \(10^{\circ}\) and \(12^{\circ}\) respectively. A second prism ' B ' deviates them through \(8^{\circ}\) and \(10^{\circ}\) respectively. The ratio of their dispersive powers is (A to B)
- A 9:13
- B \(4: 5\)
- C \(9: 11\)
- D \(8: 9\)
Answer & Solution
Correct Answer
(C) \(9: 11\)
Step-by-step Solution
Detailed explanation
Dispersive power
\(\omega=\frac{\delta_v-\delta_R}{\delta_y}, \delta_y=\frac{\delta_v+\delta_R}{2}...(i)\)
For prism A: \(\delta_y=\frac{12+10}{2}=11\)
\(\omega_{\mathrm{A}}=\frac{12-10}{11}=\frac{2}{11}\)
For prism B: \(\delta_y=\frac{8+10}{2}=9\)
\(\begin{aligned}
& \omega_{\mathrm{B}}=\frac{10-8}{9}=\frac{2}{9} \\
\therefore \quad & \frac{\omega_{\mathrm{A}}}{\omega_{\mathrm{B}}}=\frac{9}{11}
\end{aligned}\)
\(\omega=\frac{\delta_v-\delta_R}{\delta_y}, \delta_y=\frac{\delta_v+\delta_R}{2}...(i)\)
For prism A: \(\delta_y=\frac{12+10}{2}=11\)
\(\omega_{\mathrm{A}}=\frac{12-10}{11}=\frac{2}{11}\)
For prism B: \(\delta_y=\frac{8+10}{2}=9\)
\(\begin{aligned}
& \omega_{\mathrm{B}}=\frac{10-8}{9}=\frac{2}{9} \\
\therefore \quad & \frac{\omega_{\mathrm{A}}}{\omega_{\mathrm{B}}}=\frac{9}{11}
\end{aligned}\)
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