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Question

# An object is placed to the left of a lens, and a real image is formed to the right of the lens. The image is inverted relative to the object and is one-half the size of the object.What kind of lens, converging or diverging, is used to produce this image?

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Knowns The object distance $d_o$ is related with the image distance $d_i$ through

\begin{align*} \frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{f} \tag{1} \end{align*}

where $f$ is the focal length.

The magnification $m$ is defined as

\begin{align*} m=\frac{h_i}{h_o}=-\frac{d_i}{d_o} \tag{2} \end{align*}

where $h_o$ is the object height and $h_i$ is the image height.

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