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 μ 1 and μ 2 , R is the radius of curvature of the curved surface of the lenses, then the focal length of combination is

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 μ 1 and μ 2 , R is the radius of curvature of the curved surface of the lenses, then the focal length of combination is, R 2 μ 1 + μ 2, R 2 μ 1 - μ 2, R μ 1 - μ 2, 2 R μ 1 - μ 2

MARKS App · Accepted Answer

Focal length of combination 1 f = 1 f 1 + 1 f 2 … i Using lens maker's formula 1 f 2 = μ 2 - 1 1 - R - 1 ∞ = - μ 2 - 1 R 1 f 1 = μ 1 - 1 1 ∞ - 1 - R = μ 1 - 1 R or 1 f 1 = μ 1 - 1 R 1 f 2 = - μ 2 - 1 R Putting these values in Equation ( i ) , we get ⇒ 1 f = μ 1 - 1 R - μ 2 - 1 R ⇒ 1 f = μ 1 - 1 - μ 2 + 1 R ⇒ 1 f = μ 1 - μ 2 R f = R μ 1 - μ 2

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