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?
Answer & explanation
Correct answer: option 2
The condition for achromatism is
$\omega_1 P_1+\omega_2 P_2=0$
$\omega_1 P_1=-\omega_2 P_2 \Rightarrow \frac{\omega_1}{\omega_2}=\frac{P_2}{P_1}$
Now, $P_1+P_2=2 D$ or $5+P_2=2$ or $P_2=-3 D$
∴ $\frac{\omega_1}{\omega_2}=-\frac{-3}{5}=\frac{3}{5}$