Two identical thin plano-convex glass lenses (refractive index 1.5), each having radius of curvature 20 cm, are placed with their convex surfaces in contact at the centre. The intervening space is filled with oil of refractive index 1.7. The focal length of the combination is:
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Question

Two identical thin plano-convex glass lenses (refractive index 1.5), each having radius of curvature 20 cm, are placed with their convex surfaces in contact at the centre. The intervening space is filled with oil of refractive index 1.7. The focal length of the combination is:

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G1 Physics · Accepted Answer

Step 1: A glass plano-convex interface of radius R contributes (1.5 − 1)/R = 0.5/R. Step 2: The oil-filled double-concave space contributes −2(1.7 − 1)/R = −1.4/R. Step 3: Net power 1/F = (1.0 − 1.4)/R = −0.4/(0.20 m) = −2 D. Step 4: F = −0.50 m. Final answer: (C) −50 cm.