Consider three converging lenses $\mathrm{L}{1}$, $\mathrm{L}{2}$, and $\mathrm{L}{3}$ having identical geometrical construction. The refractive index of $\mathrm{L}{1}$ and $\mathrm{L}{2}$ are $\mu{1}$ and $\mu_{2}$, respectively. The upper half of the lens $\mathrm{L}{3}$ has a refractive index $\mu{1}$ and the lower half has $\mu_{2}$. A point $O$ is imaged at $O_{1}$ by the lens $\mathrm{L}{1}$ and at $O{2}$ by the lens $\mathrm{L}{2}$ placed in the same position. If $\mathrm{L}{3}$ is placed at the same place:

A There will be an image at $O_{1}$. B There will be an image at $O_{2}$. C The only image will form somewhere between $O_{1}$ and $O_{2}$. D The only image will form away from $O_{2}$.

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The correct options are:

A. There will be an image at $O_{1}$.

B. There will be an image at $O_{2}$.

The reasoning is based on the focal lengths. The focal lengths of both the upper half and the lower half of lens $\mathrm{L}3$ remain unchanged despite having different refractive indices ($\mu{1}$ for the upper half and $\mu_{2}$ for the lower half). Therefore, $\mathrm{L}_3$ will form images at the same positions as $\mathrm{L}1$ and $\mathrm{L}2$ when placed in the same location, resulting in **images forming at both $O{1}$ and $O{2}$**.

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