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Question:

One plano-convex and one plano-concave lens of 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 μ₁ and that of 2 is μ₂, what is the focal length of the combination?

R/(μ₁−μ₂)

2R/(μ₁−μ₂)

R²−(μ₁−μ₂)

R²(μ₁−μ₂)

Solution:

For 1st lens
1/f₁ = (μ₁−1)(1/∞ − 1/−R) = (μ₁−1)/R
For 2nd lens
1/f₂ = (μ₂−1)(−1/−R − 0) = (μ₂−1)/R
1/fₑq = 1/f₁ + 1/f₂
1/fₑq = R/(μ₁−1) + R/(−(μ₂−1)) ⇒ 1/fₑq = R/(μ₁−μ₂)
Hence (μ₁−μ₂)R