Two thin lenses have a combined power of +9D. When they are separated by a distance of 20 cm, their equivalent power becomes +27/5 D. The power of both the lenses in dioptre are respectively (a) 4, 5 (b) 3, 6 (c) 2, 7 (d) 1, 8

Answer: (b). In contact: P₁ + P₂ = 9. Separated: P = P₁ + P₂ - dP₁P₂. 27/5 = 9 - 0.2 P₁P₂ ⇒ P₁P₂ = 18 Numbers with sum 9 and product 18: 3 and 6. So the answer is (b) 3, 6.

Two thin lenses have a combined power of +9D. When they are separated… | MHT CET 2024 (2 May, Shift 1)

Q28MHT CET 2024 · 2 MAY · SHIFT 1Medium

Combination of Lenses

Two thin lenses have a combined power of +9D. When they are separated by a distance of 20 cm, their equivalent power becomes $+\frac{27}{5}\text{ D}$ . The power of both the lenses in dioptre are respectively

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Answer: (b)

In contact: $P_1 + P_2 = 9$ . Separated: $P = P_1 + P_2 - dP_1P_2$ .
$\frac{27}{5} = 9 - 0.2\,P_1P_2 \Rightarrow P_1P_2 = 18$
Numbers with sum 9 and product 18: $3$ and $6$ .
So the answer is (b) $3, 6$ .

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