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A plano-convex lens (focal length f2, refractive index μ2, radius of curvature R) fits exactly into a plano-concave lens (focal length f1, refractive index μ1, radius of curvature R). Their plane surfaces are parallel to each other. Then, the focal length of the combination will be:

1. f1 + f2
2. f1 - f2
3. R/(μ2 - μ1)
4. 2f1f2/(f1 + f2)

Correct answer: R/(μ2 - μ1)

Solution

Plano-convex: 1/f2 = (mu2-1)/R; plano-concave: 1/f1 = -(mu1-1)/R. In contact, 1/f = (mu2-mu1)/R, so f = R/(mu2 - mu1).

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