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

An achromatic convergent doublet of two lenses in contact has a power of + 2D. The convex lens has power + 5D. 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{ \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}}

Now, \mathrm{\mathrm{P}_1+\mathrm{P}_2=2 \mathrm{D} ~or ~5+\mathrm{P}_2=2} \mathrm{~or \mathrm{~P}_2=-3 \mathrm{D}}
\mathrm{ \therefore \frac{\omega_1}{\omega_2}=-\frac{-3}{5}=\frac{3}{5} }

Posted by

Nehul

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