Two identical symmetric double convex lenses of focal length f are cut into two equal parts L₁, L₂ by AB plane and L₃, L₄ by XY plane as shown in figure respectively. The ratio of focal lengths of lenses L₁ and L₃ is

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(1) 1 : 2. AB is along the principal axis: L₁ keeps both curved faces, so f₁=f. XY is the plane of the lens: L₃ is plano-convex with one curved face, so 1/(f₃)=(μ-1)/R=1/(2f), f₃=2f. f₁:f₃=1:2

Two identical symmetric double convex lenses of focal length f are cut into two equal parts L₁, L₂ by AB plane and L₃, L₄ by XY plane as shown in figure respectively. The ratio of focal lengths of lenses L₁ and L₃ is

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