Question

Two thin lenses, when in contact, produce a combination of power + 10 D. When they are 0.25 m apart, the power reduces to + 6 D. The focal length of the lenses are.......m and........m.

Answer 1

When the lenses are in contact, the power of the system is
$P=P_1+P_{2}or{P}_1+P_2=\mathrm{10...}(i)$
=41​m
The power is $P=P_1+P_2-d{P}_1{P}_2$
$or{P}_1+P_2-\frac{P_1{P}_2}{4}=\mathrm{6...}(ii)$
Solving Eqs. (i) and (ii), we can find that $P_1=8$ D and
$P_2=D$
$\therefore f_1=\frac{1}{8}m=0.125m\Rightarrow f_2=\frac{1}{2}m=0.5m$