A convex lens forms a real image of a point object placed on its principal axis. If the upper half of the lens is painted black,

Consider three converging lenses $L_1, L_2$ and $L_3$ having identical geometrical construction. The index of refraction of $L_1$ and $L_2$ are ${\mu }_1$ and ${\mu }_2$, respectively. The upper half of the lens $L_3$ has a refractive index ${\mu }_1$ and the lower half has ${\mu }_2$. A point object $O$ imaged at $O_1$ by the lens $L_1$ and at $O_2$ by the lens $L_2$ placed in same position. If, $L_3$ is placed at the same place,