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Two plano-convex lenses, labelled 1 and 2, are made of glass with refractive index 1.5. Their radii of curvature are 25 cm and 20 cm, respectively. They are kept in contact with their curved faces facing one another, and the gap between them is occupied by a liquid of refractive index 4/3. The resulting system behaves as

1. a convex lens with focal length 70 cm
2. a concave lens with focal length 70 cm
3. a concave lens with focal length 66.6 cm
4. a convex lens with focal length 66.6 cm

Correct answer: a convex lens with focal length 66.6 cm

Solution

f1 = 25/0.5 = 50 cm (P=0.02), f2 = 20/0.5 = 40 cm (P=0.025). The 4/3 liquid forms a biconcave lens: 1/f = (1/3)(1/(-25) - 1/20) = -0.03. Total P = 0.02 + 0.025 - 0.03 = 0.015, so f = +66.6 cm, a convex lens.

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