Question

An object is placed at a distance of $\frac{f}{2}$ from a convex lens. The image will be
(1) At one of the foci, virtual and double its size.
(2) At $\frac{3f}{2}$, real and inverted.

Answer 1

$\frac{1}{f}=\frac{1}{f}+\frac{1}{v}$
$\frac{1}{f}=\frac{2}{f}+\frac{1}{v}$
$-\frac{2}{f}=\frac{1}{f}+\frac{1}{v}$
$v=-f$
The image is virtual and on the negative focal point. (The image is upright and magnified by 2.)