Question

An achromatic doublet is a converging lens of equivalent focal length $100cm$. If the dispersive powers of the material of the lenses are in the ratio $1:2$. The focal lengths of the two lenses are:

Answer 1

$f=100cm$, Now, from question: $f_1:f_2=1:2⟹f_2=2f_1$

For an achromatic combination,
$\frac{f_1}{w_1}+\frac{f_2}{w_2}=0$
Also, the effective focal length of the combination will be,
$\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}$
Solving these simultaneously and substituting the values,
the obtained focal lengths are: $f_o=50and{f}_e=-100$