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Two thin lenses of powers $+5\ \text{D}$ and $-2\ \text{D}$ are placed in contact. What is the focal length of the combination?
A$\approx 0.14\ \text{m}$
B$\approx 0.50\ \text{m}$
C$\approx 3.00\ \text{m}$
D$\approx 0.33\ \text{m}$
Answer & Solution
Correct answer: D. $\approx 0.33\ \text{m}$
1. Powers of lenses in contact add: $P = P_1 + P_2$.
2. Substitute: $P = (+5) + (-2) = +3\ \text{D}$.
3. Focal length is $f = \dfrac{1}{P} = \dfrac{1}{3} \approx 0.33$ m.
4. Adding the magnitudes (7 D) would give $0.14$ m, a trap that ignores the sign.
5. The value $3$ m mistakes the power for the focal length.
_Source: Samacheer Kalvi (TN SCERT) Class 10 Science, Unit 2 Optics "Power of a Lens", p.30_
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