Two thin lenses of focal lengths $+10$ cm and $+20$ cm are placed in contact. The power of the combination, in diopters, is:
A$5$ D
B$10$ D
C$15$ D
D$20$ D
Answer & Solution
Correct answer: C. $15$ D
**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.
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