Concave and convex lenses are placed touching each other. The ratio… | MHT CET 2024 (9 May, Shift 2)

Q27MHT CET 2024 · 9 MAY · SHIFT 2Medium

Combination of Lenses

Concave and convex lenses are placed touching each other. The ratio of magnitudes of their power is $2 : 3$ . The focal length of the system is 30 cm. The focal lengths of individual lens are

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Answer: (b)

System focal length is $+30\text{ cm}$ , so the convex lens is stronger: $P_{\text{convex}} = 3k$ , $P_{\text{concave}} = -2k$ .
$P = 3k - 2k = k = \frac{1}{0.3}\text{ D}$
$f_{\text{convex}} = \frac{1}{3k} = \frac{0.3}{3} = 10\text{ cm}$ , $f_{\text{concave}} = -\frac{0.3}{2} = -15\text{ cm}$
So the answer is (b) $10\text{ cm}, -15\text{ cm}$ .

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