One plano-convex and one plano-concave lens of the same radius of curvature $R$ but of different materials are joined side by side as shown in the figure. If the refractive index of the material of $1$ is $μ_{1}$ and that of $2$ is $μ_{2}$ , then the focal length of the combination is:

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From lens maker’s formula, 1 f = μ - 1 1 R 1 - 1 R 2 1 f 1 = μ 1 - 1 1 ∞ - 1 - R = μ 1 - 1 R 1 f 2 = μ 2 - 1 1 - R - 1 ∞ = - μ 2 - 1 R 1 f e q = 1 f 1 + 1 f 2 = μ 1 - 1 R - μ 2 - 1 R = μ 1 - μ 2 R f e q = R μ 1 - μ 2

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