Two thin lenses of focal lengths $+10$ cm and $+20$ cm are placed in contact. The power of the combination, in diopters, is:

**For thin lenses in contact**, powers add: $P = P_1 + P_2$. $P_1 = \dfrac{1}{f_1\text{ (m)}} = \dfrac{1}{0.10} = 10$ D. $P_2 = \dfrac{1}{0.20} = 5$ D. $P_{\text{total}} = 10 + 5 = 15$ D. Equivalently, $\dfrac{1}{F} = \dfrac{1}{10} + \dfrac{1}{20} = \dfrac{3}{20}$ giving $F = \dfrac{20}{3}$ cm $\approx 6.67$ cm so $P = \dfrac{100}{6.67} = 15$ D.