Physics - Geometrical Optics Question with Solution | TestHub

Power of the combination, $P=+2D$

Power of the convex (convergent) lens, $P_1=+5D$

Power of the divergent lens, $P_2=P-P_1=2-5=-3D$

For an achromatic doublet, the condition is $\frac{{\omega }_1}{f_1}+\frac{{\omega }_2}{f_2}=0$

Since $P=\frac{1}{f}$, we have ${\omega }_1{P}_1+{\omega }_2{P}_2=0$

Substituting the values of $P_1$ and $P_2$:

${\omega }_1(5)+{\omega }_2(-3)=0$

$5{\omega }_1=3{\omega }_2$

$\frac{{\omega }_1}{{\omega }_2}=\frac{3}{5}$

The ratio of the dispersive powers is $3:5$.

Answer: $3:5$