A plano-convex lens fits exactly into a plano-concave lens. Their plane surfaces are parallel to each other. The lenses are made of different materials of refractive indices μ₁ and μ₂, and R is the radius of curvature of the curved surface of the lenses. The focal length of the combination is:
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Question

A plano-convex lens fits exactly into a plano-concave lens. Their plane surfaces are parallel to each other. The lenses are made of different materials of refractive indices μ₁ and μ₂, and R is the radius of curvature of the curved surface of the lenses. The focal length of the combination is:

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G1 Physics · Accepted Answer

Step 1: Add powers of both thin lens elements at the curved interface. Step 2: Plano-convex contribution: (μ₁ − 1)/R. Plano-concave contribution: −(μ₂ − 1)/R. Step 3: 1/F = (μ₁ − μ₂)/R. Final answer: (A) F = R/(μ₁ − μ₂).