devarshi-dt-logo

Question:

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?

R²(μ₁−μ₂)

R(μ₂−μ₁)

R²(μ₁+μ₂)

R(μ₁−μ₂)

Solution:

From the lensmaker formula for plano convex lens,
1/f₁ = (μ₁-1)(1/R)
For plano concave lens,
1/f₂ = −(μ₂-1)(1/R)
For the combination,
1/feq = 1/f₁ + 1/f₂ = (μ₁−1)(1/R) − (μ₂−1)(1/R) = (μ₁ − μ₂)(1/R)
This gives us
feq = R/(μ₁−μ₂)