Suppose three converging lenses L₁ , L₂ , and L₃ share an identical geometrical construction. The refractive indices of L₁ and L₂ are ₁ and ₂ , respectively. As shown in the figure, the upper half of lens L₃ has a refractive index ₁ , while the lower half has ₂ . When placed in a specific position, lens L₁ forms an image of a point object O at O₁ , and lens L₂ placed in the same position forms an image at O₂ . If len

Step-by-step solution

The focal length of a lens is given by the lens maker's formula: 1 f = ( - 1) ( 1 R₁ - 1 R₂ ) For lens L₁ with refractive index ₁ , the image of object O is formed at O₁ . For lens L₂ with refractive index ₂ , the image of object O is formed at O₂ . Lens L₃ is composed of two halves: the upper half has a refractive index ₁ and the lower half has a refractive index ₂ . The upper half of L₃ will refract the light rays exactly as lens L₁ does, converging them to form an image at O₁ . The lower half of L₃ will refract