A prism of a certain angle deviates the red and blue rays by 8 and...

A prism of a certain angle deviates the red and blue rays by 8 and 12 , respectively. Another prism of the same angle deviates the red and blue rays by 10 and 14 , respectively. The prisms are small angled and made of different materials. The dispersive power of the materials of the prisms are in the ratio

Options

A5:6
B9:11
C6:5
D11:9

Correct answer

C. 6:5

Step-by-step solution

For prism 1,

\begin{aligned} & \delta=\frac{\delta_B+\delta_R}{2}=\frac{12+8}{2}=10 \\ & \text{ [given, } \delta_R=8, \delta_B=12 \text{ ] } \\ & \therefore \quad \omega_1=\frac{\delta_B-\delta_R}{\delta}=\frac{12-8}{10}=\frac{4}{10}=\frac{2}{5} \\ & \end{aligned}

For prism 2,

\begin{aligned} & \delta=\frac{\delta_B+\delta_R}{2}=\frac{14+10}{2}=12 \\ \therefore \quad & \omega_2=\frac{\delta_B-\delta_R}{\delta}=\frac{14-10}{12}=\frac{1}{3}\end{aligned}

So,

\quad \frac{\omega_1}{\omega_2}=\frac{2 / 5}{1 / 3}=\frac{6}{5}

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