A plano convex lens fits exactly in to a plano concave lens. Their plane surfaces are parallel to each other. Lenses are made up of different materials of refractive indices ' n₁ ' n₂ ' and ' R ' is the radius of curvature of the curved surface of lenses. Focal length of the combination is

Step-by-step solution

Focal length analysis of the lens combination The focal length of each lens is determined using the Lens Maker's Formula: 1 f = (n-1) ( 1 R₁ - 1 R₂ ) , assuming light travels left to right. For the plano-convex lens, the first surface is flat ( R₁ = ) and the second surface is convex with R₂ = -R . 1 f₁ = (n₁ - 1) ( 1 - 1 -R ) = n₁ - 1 R The plano-concave lens interfaces with the convex surface, giving R₁ = -R for its concave surface, while its second surface is flat ( R₂ = ). 1 f₂ = (n₂ - 1) ( 1 -R - 1 ) = - n₂ -