Q142 / 180 · JIPMER 2016 · Physics

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

  • A
    5:6
  • B
    9:11
  • Correct answer
    C
    6:5
  • D
    11:9

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

Hence, the correct answer is option: 'C'.

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