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

Step-by-step solution

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