Q. 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
A) R/(2(μ₁ + μ₂))
B) R/(2(μ₁ − μ₂))
C) R/(μ₁ − μ₂)
D) 2R/(μ₂ − μ₁)
Explanation
[Solution from source] Plano-convex: 1/f₁ = (μ₁ − 1)/R; plano-concave of the same curvature: 1/f₂ = −(μ₂ − 1)/R. In contact: 1/f = (μ₁ − μ₂)/R, so f = R/(μ₁ − μ₂). A factor of 2 would appear only for double-curved lenses. Answer (3).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.