Suppose three converging lenses L_1 , L_2 , and L_3 share an...

The focal length of a lens is given by the lens maker's formula:

$\dfrac{1}{f} = (\mu - 1)\left(\dfrac{1}{R_1} - \dfrac{1}{R_2}\right)$

For lens $L_1$ with refractive index $\mu_1$, the image of object $O$ is formed at $O_1$.

For lens $L_2$ with refractive index $\mu_2$, the image of object $O$ is formed at $O_2$.

Lens $L_3$ is composed of two halves: the upper half has a refractive index $\mu_1$ and the lower half has a refractive index $\mu_2$.

The upper half of $L_3$ will refract the light rays exactly as lens $L_1$ does, converging them to form an image at $O_1$.

The lower half of $L_3$ will refract the light rays exactly as lens $L_2$ does, converging them to form an image at $O_2$.

Since each half of the lens forms a complete image of the object independently (with reduced intensity), two distinct images will be formed: one at $O_1$ and another at $O_2$.