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An achromatic convergent doublet of two lenses in contact has a power of \mathrm{+ 2\ D}. The convex lens has power \mathrm{+ 5\ D}. What is the ratio of the dispersive powers of the convergent and divergent lenses?

Option: 1

2:5


Option: 2

3:5


Option: 3

5:2


Option: 4

5:3


Answers (1)

best_answer

The condition for achromatism is
\mathrm{\begin{aligned} & \mathrm{\omega_1 P_1+\omega_2 P_2=0} \\ &\mathrm{ \omega_1 P_1=-\omega_2 P_2 \Rightarrow \frac{\omega_1}{\omega_2}=-\frac{P_2}{P_1}} \end{aligned}}
\mathrm{Now, P_1+P_2=2 D\ or\ 5+P_2=2\ or\ P_2=-3 D} \\ \mathrm{\therefore \quad \frac{\omega_1}{\omega_2}=-\frac{-3}{5}=\frac{3}{5}}

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Nehul

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