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
$P = P_1 + P_2 or P_1 + P_2 = 10 ...(i)$
The power is $P = P_1 + P_2 - d P_1 P_2$
$or P_1+P_2-\frac{P_1 P_2}{4}=6 ...(ii)$
Solving Eqs. (i) and (ii), we can find that $P_1 = 8$ D and
$P_2=D$
$\therefore \, \, \, \, \, f_1=\frac{1}{8}m=0.125m \, \, \, \, \, \, \Rightarrow f_2=\frac{1}{2}m =0.5m$