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A plano convex lens fits exactly into a plano concave lens. Their plane surfaces are parallel to each other. If 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, then the focal length of the combination is

1. R / (2(μ₁ − μ₂))
2. R / (μ₁ − μ₂)
3. 2R / (μ₂ − μ₁)
4. R / (2(μ₁ + μ₂))

Correct answer: R / (2(μ₁ − μ₂))

Solution

The focal length of the combination is determined by the lens maker's formula. Since the lenses are in contact and their plane surfaces are parallel, the effective focal length depends on the difference in refractive indices and the radius of curvature. The correct formula is R / (2(μ₁ − μ₂)).

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