Question

Two thin lenses, when in contact, produce a combination of power $+10$ diopters. Whey they are $0.25m$ apart, the power reduces to $+6$ diopters. The focal lengths of the lenses are $m$ and ________ $m$.

Answer 1

Case $I$:

$P=P_1+P_{2}10=P_1+P_2-\left(i\right)$

Case $II$;

$6=P_1+P_2-0.25P_1{P}_2\Rightarrow P_1{P}_2=16P_1=\frac{16}{P_2}-\left(ii\right)$

Solving $\left(i\right)$ and $\left(ii\right)$

$P_1=2$

$f_1=\frac{1}{2}$m

$P_2=8$

$f_2=\frac{1}{8}$m